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Fast convergence of inertial dynamics and algorithms with asymptotic vanishing viscosity

Mathematical programming, ISSN 1436-4646, 2016, Volume 168, Issue 1-2, pp. 123 - 175

In a Hilbert space setting $${{\mathcal {H}}}$$ H , we study the fast convergence properties as $$t \rightarrow + \infty $$ tâ†’+âˆž of the trajectories of the...

65K05 | Inertial dynamics | Theoretical, Mathematical and Computational Physics | Mathematics | Gradient flows | Dynamical systems | 34D05 | Mathematical Methods in Physics | 90C30 | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | Convex optimization | 90C25 | Numerical Analysis | Fast convergent methods | Vanishing viscosity | 65K10 | Combinatorics | 49M25 | Nesterov method | SYSTEM | MATHEMATICS, APPLIED | MAXIMAL MONOTONE-OPERATORS | PROXIMAL METHOD | BEHAVIOR | EQUATIONS | COMPUTER SCIENCE, SOFTWARE ENGINEERING | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | Analysis | Algorithms | Differential equations | Hilbert space | Trajectories | Nonlinear programming | Convergence | Viscous damping | Optimization and Control

65K05 | Inertial dynamics | Theoretical, Mathematical and Computational Physics | Mathematics | Gradient flows | Dynamical systems | 34D05 | Mathematical Methods in Physics | 90C30 | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | Convex optimization | 90C25 | Numerical Analysis | Fast convergent methods | Vanishing viscosity | 65K10 | Combinatorics | 49M25 | Nesterov method | SYSTEM | MATHEMATICS, APPLIED | MAXIMAL MONOTONE-OPERATORS | PROXIMAL METHOD | BEHAVIOR | EQUATIONS | COMPUTER SCIENCE, SOFTWARE ENGINEERING | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | Analysis | Algorithms | Differential equations | Hilbert space | Trajectories | Nonlinear programming | Convergence | Viscous damping | Optimization and Control

Journal Article

IEEE transactions on automatic control, ISSN 1558-2523, 2019, Volume 64, Issue 6, pp. 2224 - 2239

We present novel results on the solution of a class of leavable, undiscounted optimal control problems in the minimax sense for nonlinear, continuous-state,...

discrete abstraction | Upper bound | Perturbation methods | Optimal control | symbolic control | Aerospace electronics | Approximate dynamic programming | difference inclusion | nonlinear system | Adaptive control | Convergence | Problems | Minimax technique | Parameters | Discretization | Production planning | Upper bounds | Control systems | Feedback control | Markov analysis | Continuity (mathematics)

discrete abstraction | Upper bound | Perturbation methods | Optimal control | symbolic control | Aerospace electronics | Approximate dynamic programming | difference inclusion | nonlinear system | Adaptive control | Convergence | Problems | Minimax technique | Parameters | Discretization | Production planning | Upper bounds | Control systems | Feedback control | Markov analysis | Continuity (mathematics)

Journal Article

Mathematical programming, ISSN 1436-4646, 2015, Volume 159, Issue 1-2, pp. 81 - 107

We introduce new optimized first-order methods for smooth unconstrained convex minimization. Drori and Teboulle (Math Program 145(1â€“2):451â€“482, 2014. doi:...

68Q25 | Fast gradient methods | Theoretical, Mathematical and Computational Physics | Convergence bound | Mathematics | 90C20 | Mathematical Methods in Physics | First-order algorithms | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | 90C25 | Numerical Analysis | 90C22 | Smooth convex minimization | Combinatorics | 90C60 | 49M25 | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | Electrical engineering | Computer science | Algorithms | Methods | Studies | Numerical analysis | Convergence | Mathematical programming | Computation | Mathematical analysis | Minimization | Mathematical models | Optimization | Mathematics - Optimization and Control

68Q25 | Fast gradient methods | Theoretical, Mathematical and Computational Physics | Convergence bound | Mathematics | 90C20 | Mathematical Methods in Physics | First-order algorithms | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | 90C25 | Numerical Analysis | 90C22 | Smooth convex minimization | Combinatorics | 90C60 | 49M25 | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | Electrical engineering | Computer science | Algorithms | Methods | Studies | Numerical analysis | Convergence | Mathematical programming | Computation | Mathematical analysis | Minimization | Mathematical models | Optimization | Mathematics - Optimization and Control

Journal Article

Discrete and Continuous Dynamical Systems- Series A, ISSN 1078-0947, 03/2018, Volume 38, Issue 3, pp. 1161 - 1185

Discrete and Dynamical Systems A, 38.3 (2018), 1161-1185 In this article we investigate a first order reparametrization-invariant Sobolev metric on the space...

Shape analysis | Solitons | Curves | Elastic metric | Mathematics - Differential Geometry

Shape analysis | Solitons | Curves | Elastic metric | Mathematics - Differential Geometry

Journal Article

Applied Mathematics & Optimization, ISSN 0095-4616, 12/2017, Volume 76, Issue 3, pp. 565 - 592

The principal-agent problem in economics leads to variational problems subject to global constraints of b-convexity on the admissible functions, capturing the...

65K15 | Systems Theory, Control | Theoretical, Mathematical and Computational Physics | Principal-agent problem | Iterated projections | Mathematics | Mathematical Methods in Physics | Convex envelopes | Calculus of Variations and Optimal Control; Optimization | 90C25 | Numerical and Computational Physics, Simulation | 49M25 | Convexity constraint | Dykstraâ€™s algorithm | b -convexity constraint | b-convexity constraint | MATHEMATICS, APPLIED | REGULARITY | ALGORITHM | ENVELOPE | PROBLEMS SUBJECT | Dykstra's algorithm | MONOTONE-OPERATORS | Algorithms | Mathematical analysis | Numerical methods | Convexity

65K15 | Systems Theory, Control | Theoretical, Mathematical and Computational Physics | Principal-agent problem | Iterated projections | Mathematics | Mathematical Methods in Physics | Convex envelopes | Calculus of Variations and Optimal Control; Optimization | 90C25 | Numerical and Computational Physics, Simulation | 49M25 | Convexity constraint | Dykstraâ€™s algorithm | b -convexity constraint | b-convexity constraint | MATHEMATICS, APPLIED | REGULARITY | ALGORITHM | ENVELOPE | PROBLEMS SUBJECT | Dykstra's algorithm | MONOTONE-OPERATORS | Algorithms | Mathematical analysis | Numerical methods | Convexity

Journal Article

Advances in calculus of variations, ISSN 1864-8266, 2019, Volume 12, Issue 1, pp. 1 - 29

We consider an evolution in phase-field fracture which combines, in a system of PDEs, an irreversible gradient-flow for the phase-field variable with the...

brittle fracture | quasi-static BV-evolution | Phase-field | gradient flow | 74R10 | 49M25 | 35M86 | Evolution | Equilibrium equations | Gradient flow

brittle fracture | quasi-static BV-evolution | Phase-field | gradient flow | 74R10 | 49M25 | 35M86 | Evolution | Equilibrium equations | Gradient flow

Journal Article

Numerische Mathematik, ISSN 0029-599X, 11/2016, Volume 134, Issue 3, pp. 611 - 636

Gradient flows in the Wasserstein space have become a powerful tool in the analysis of diffusion equations, following the seminal work of Jordan, Kinderlehrer...

Mathematical Methods in Physics | Numerical Analysis | Theoretical, Mathematical and Computational Physics | Appl.Mathematics/Computational Methods of Engineering | 52B55 | Mathematics, general | Mathematics | Numerical and Computational Physics, Simulation | 49M25 | Analysis of PDEs

Mathematical Methods in Physics | Numerical Analysis | Theoretical, Mathematical and Computational Physics | Appl.Mathematics/Computational Methods of Engineering | 52B55 | Mathematics, general | Mathematics | Numerical and Computational Physics, Simulation | 49M25 | Analysis of PDEs

Journal Article

Archive for Rational Mechanics and Analysis, ISSN 0003-9527, 12/2015, Volume 218, Issue 3, pp. 1263 - 1329

This paper aims at building a unified framework to deal with a wide class of local and nonlocal translation-invariant geometric flows. We introduce a class of...

Mechanics | Physics, general | Fluid- and Aerodynamics | Statistical Physics, Dynamical Systems and Complexity | Theoretical, Mathematical and Computational Physics | Physics | EXISTENCE | VISCOSITY SOLUTIONS | MATHEMATICS, APPLIED | MECHANICS | SET | MOTION | IMPLICIT TIME DISCRETIZATION | FRONT PROPAGATION | UNIQUENESS | Numerical Analysis | Mathematics

Mechanics | Physics, general | Fluid- and Aerodynamics | Statistical Physics, Dynamical Systems and Complexity | Theoretical, Mathematical and Computational Physics | Physics | EXISTENCE | VISCOSITY SOLUTIONS | MATHEMATICS, APPLIED | MECHANICS | SET | MOTION | IMPLICIT TIME DISCRETIZATION | FRONT PROPAGATION | UNIQUENESS | Numerical Analysis | Mathematics

Journal Article

Numerische Mathematik, ISSN 0945-3245, 2000, Volume 87, Issue 2, pp. 247 - 282

The convergence rate is determined for Runge-Kutta discretizations of nonlinear control problems. The analysis utilizes a connection between the Kuhn-Tucker...

Mathematics Subject Classification : 49M25, 65L06 | DISCRETE APPROXIMATIONS | MATHEMATICS, APPLIED | CONVERGENCE | NONLINEAR OPTIMAL-CONTROL | SUFFICIENT CONDITIONS | STABILITY

Mathematics Subject Classification : 49M25, 65L06 | DISCRETE APPROXIMATIONS | MATHEMATICS, APPLIED | CONVERGENCE | NONLINEAR OPTIMAL-CONTROL | SUFFICIENT CONDITIONS | STABILITY

Journal Article

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Convergence Rate for a Gauss Collocation Method Applied to Unconstrained Optimal Control

Journal of Optimization Theory and Applications, ISSN 0022-3239, 6/2016, Volume 169, Issue 3, pp. 801 - 824

A local convergence rate is established for an orthogonal collocation method based on Gauss quadrature applied to an unconstrained optimal control problem. If...

65K05 | Orthogonal collocation | Mathematics | Theory of Computation | Gauss collocation method | Optimization | 90C30 | Calculus of Variations and Optimal Control; Optimization | Optimal control | Convergence rate | Applications of Mathematics | Engineering, general | Operation Research/Decision Theory | 49M37 | 49M25 | Methods | Aerospace engineering | Studies | Control theory | Collocation | Collocation methods | Mathematical models | Convexity | Convergence | Quadratures | Mathematics - Optimization and Control

65K05 | Orthogonal collocation | Mathematics | Theory of Computation | Gauss collocation method | Optimization | 90C30 | Calculus of Variations and Optimal Control; Optimization | Optimal control | Convergence rate | Applications of Mathematics | Engineering, general | Operation Research/Decision Theory | 49M37 | 49M25 | Methods | Aerospace engineering | Studies | Control theory | Collocation | Collocation methods | Mathematical models | Convexity | Convergence | Quadratures | Mathematics - Optimization and Control

Journal Article

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Gradient Methods on Strongly Convex Feasible Sets and Optimal Control of Affine Systems

Applied Mathematics and Optimization, ISSN 0095-4616, 2018, Volume 81, Issue 3, pp. 1021 - 1054

The paper presents new results about convergence of the gradient projection and the conditional gradient methods for abstract minimization problems on strongly...

Gradient methods | Affine control systems | Bangâ€“bang control | Numerical methods | Optimal control | Mathematical programming | MATHEMATICS, APPLIED | Bang-bang control | EULER DISCRETIZATION | DISCRETE APPROXIMATIONS | REGULARIZATION | Control theory | Convexity | Discretization | Optimization | Convergence | 90C25 | 90C48 | 49M37 | 49M25

Gradient methods | Affine control systems | Bangâ€“bang control | Numerical methods | Optimal control | Mathematical programming | MATHEMATICS, APPLIED | Bang-bang control | EULER DISCRETIZATION | DISCRETE APPROXIMATIONS | REGULARIZATION | Control theory | Convexity | Discretization | Optimization | Convergence | 90C25 | 90C48 | 49M37 | 49M25

Journal Article

Journal of optimization theory and applications, ISSN 1573-2878, 2018, Volume 182, Issue 3, pp. 1171 - 1185

This paper deals with an opinion formation model, that obeys a nonlinear system of fractional-order differential equations. We introduce a virtual leader in...

26A33 | Mathematics | Theory of Computation | Fractional derivatives | Optimization | 49K99 | 39A99 | Calculus of Variations and Optimal Control; Optimization | Operations Research/Decision Theory | Optimal control | Consensus problem | Applications of Mathematics | Engineering, general | Opinion formation models | Variational integrators | 49M25 | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | DYNAMICS | CONSENSUS | TIME | Computer science | Models | Analysis | Differential equations | Nonlinear systems

26A33 | Mathematics | Theory of Computation | Fractional derivatives | Optimization | 49K99 | 39A99 | Calculus of Variations and Optimal Control; Optimization | Operations Research/Decision Theory | Optimal control | Consensus problem | Applications of Mathematics | Engineering, general | Opinion formation models | Variational integrators | 49M25 | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | DYNAMICS | CONSENSUS | TIME | Computer science | Models | Analysis | Differential equations | Nonlinear systems

Journal Article

Set-Valued and Variational Analysis, ISSN 1877-0533, 3/2015, Volume 23, Issue 1, pp. 69 - 86

The paper is devoted to the study of a new class of optimal control problems governed by the classical Moreau sweeping process with the new feature that the...

Variational analysis | Discrete approximations | Mathematics | Moving controlled polyhedra | Sweeping process | Geometry | 90C30 | Dissipative differential inclusions | 49J53 | 49J52 | Analysis | Optimal control | 49M25 | 49K24 | MATHEMATICS, APPLIED

Variational analysis | Discrete approximations | Mathematics | Moving controlled polyhedra | Sweeping process | Geometry | 90C30 | Dissipative differential inclusions | 49J53 | 49J52 | Analysis | Optimal control | 49M25 | 49K24 | MATHEMATICS, APPLIED

Journal Article

Mathematical programming, ISSN 1436-4646, 2013, Volume 145, Issue 1-2, pp. 451 - 482

We introduce a novel approach for analyzing the worst-case performance of first-order black-box optimization methods. We focus on smooth unconstrained convex...

Performance of first-order algorithms | Heavy Ball method | 68Q25 | Theoretical, Mathematical and Computational Physics | Mathematics | Duality | Complexity | 90C20 | Mathematical Methods in Physics | Fast gradient schemes | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | 90C25 | Numerical Analysis | 90C22 | Semidefinite relaxations | Smooth convex minimization | Combinatorics | Rate of convergence | 90C60 | 49M25 | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | DYNAMICAL-SYSTEM | Analysis | Methods | Algorithms | Studies | Semidefinite programming | Mathematical analysis | Minimization | Optimization | Mathematical programming

Performance of first-order algorithms | Heavy Ball method | 68Q25 | Theoretical, Mathematical and Computational Physics | Mathematics | Duality | Complexity | 90C20 | Mathematical Methods in Physics | Fast gradient schemes | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | 90C25 | Numerical Analysis | 90C22 | Semidefinite relaxations | Smooth convex minimization | Combinatorics | Rate of convergence | 90C60 | 49M25 | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | DYNAMICAL-SYSTEM | Analysis | Methods | Algorithms | Studies | Semidefinite programming | Mathematical analysis | Minimization | Optimization | Mathematical programming

Journal Article

Journal of optimization theory and applications, ISSN 1573-2878, 2019, Volume 182, Issue 2, pp. 730 - 767

This paper deals with a bilevel approach of the location-allocation problem with dimensional facilities. We present a general model that allows us to consider...

Heuristics | Mathematics | Theory of Computation | Optimal transport mass | Optimization | Bilevel optimization | 90B85 | 90C30 | Calculus of Variations and Optimal Control; Optimization | Operations Research/Decision Theory | Mixed-integer programming | 90B80 | Applications of Mathematics | Engineering, general | 49M25 | Dimensional facilities | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | ALGORITHM | POWER | OPTIMAL TRANSPORT | Domains | Allocations | Approximations

Heuristics | Mathematics | Theory of Computation | Optimal transport mass | Optimization | Bilevel optimization | 90B85 | 90C30 | Calculus of Variations and Optimal Control; Optimization | Operations Research/Decision Theory | Mixed-integer programming | 90B80 | Applications of Mathematics | Engineering, general | 49M25 | Dimensional facilities | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | ALGORITHM | POWER | OPTIMAL TRANSPORT | Domains | Allocations | Approximations

Journal Article

Numerische Mathematik, ISSN 0029-599X, 12/2019, Volume 143, Issue 4, pp. 943 - 984

We present a systematic approach to the optimal placement of finitely many sensors in order to infer a finite-dimensional parameter from point evaluations of...

Mathematical Methods in Physics | 49K20 | 65K05 | 62K05 | 35R30 | Numerical Analysis | Theoretical, Mathematical and Computational Physics | Mathematical and Computational Engineering | Mathematics, general | Mathematics | Numerical and Computational Physics, Simulation | 49M25

Mathematical Methods in Physics | 49K20 | 65K05 | 62K05 | 35R30 | Numerical Analysis | Theoretical, Mathematical and Computational Physics | Mathematical and Computational Engineering | Mathematics, general | Mathematics | Numerical and Computational Physics, Simulation | 49M25

Journal Article

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Convergence rate for a Radau hp collocation method applied to constrained optimal control

Computational optimization and applications, ISSN 1573-2894, 2019, Volume 74, Issue 1, pp. 275 - 314

For control problems with control constraints, a local convergence rate is established for an hp-method based on collocation at the Radau quadrature points in...

65K05 | Radau collocation | Orthogonal collocation | Mathematics | Statistics, general | Optimization | 90C30 | Operations Research/Decision Theory | Convex and Discrete Geometry | Optimal control | Convergence rate | Operations Research, Management Science | 49M37 | 49M25 | hp Collocation | MATHEMATICS, APPLIED | P-VERSION | APPROXIMATIONS | STABILITY | 1-DIMENSION | COSTATE ESTIMATION | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | FINITE-ELEMENT-METHOD | DIRECT TRAJECTORY OPTIMIZATION | Methods | Resveratrol | Collocation methods | Polynomials | Convexity | Convergence

65K05 | Radau collocation | Orthogonal collocation | Mathematics | Statistics, general | Optimization | 90C30 | Operations Research/Decision Theory | Convex and Discrete Geometry | Optimal control | Convergence rate | Operations Research, Management Science | 49M37 | 49M25 | hp Collocation | MATHEMATICS, APPLIED | P-VERSION | APPROXIMATIONS | STABILITY | 1-DIMENSION | COSTATE ESTIMATION | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | FINITE-ELEMENT-METHOD | DIRECT TRAJECTORY OPTIMIZATION | Methods | Resveratrol | Collocation methods | Polynomials | Convexity | Convergence

Journal Article

Journal of Global Optimization, ISSN 0925-5001, 9/2019, Volume 75, Issue 1, pp. 199 - 225

We present a framework wherein the trajectory optimization problem (or a problem involving calculus of variations) is formulated as a search problem in a...

Randomized search algorithm | Mathematics | Brachistochrone problem | Optimization | Trajectory optimization | Global optimization | Quantum computation | 81P68 | Operations Research/Decision Theory | Computer Science, general | 49M25 | Calculus of variations | Real Functions | PURE ADAPTIVE SEARCH | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | ALGORITHM | Usage | Analysis | Algorithms | Time dependence | Quantum computing | Randomization | Discretization | Search algorithms | Dependent variables | Independent variables | Comparative studies

Randomized search algorithm | Mathematics | Brachistochrone problem | Optimization | Trajectory optimization | Global optimization | Quantum computation | 81P68 | Operations Research/Decision Theory | Computer Science, general | 49M25 | Calculus of variations | Real Functions | PURE ADAPTIVE SEARCH | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | ALGORITHM | Usage | Analysis | Algorithms | Time dependence | Quantum computing | Randomization | Discretization | Search algorithms | Dependent variables | Independent variables | Comparative studies

Journal Article

Journal of optimization theory and applications, ISSN 1573-2878, 2019, Volume 182, Issue 2, pp. 439 - 472

The paper is mostly devoted to applications of a novel optimal control theory for perturbed sweeping/Moreau processes to two practical dynamical models. The...

Variational analysis | Necessary optimality conditions | Discrete approximations | Mathematics | Theory of Computation | Optimization | Sweeping process | Robotics | 70B15 | 90B10 | 49J53 | Calculus of Variations and Optimal Control; Optimization | Operations Research/Decision Theory | Optimal control | Traffic flows | Applications of Mathematics | Engineering, general | 49M25 | 49K24 | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | Robotics industry | Analysis | Robots | Sweeping | Traffic flow | Traffic models | Traffic control | Control theory | Robot dynamics

Variational analysis | Necessary optimality conditions | Discrete approximations | Mathematics | Theory of Computation | Optimization | Sweeping process | Robotics | 70B15 | 90B10 | 49J53 | Calculus of Variations and Optimal Control; Optimization | Operations Research/Decision Theory | Optimal control | Traffic flows | Applications of Mathematics | Engineering, general | 49M25 | 49K24 | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | Robotics industry | Analysis | Robots | Sweeping | Traffic flow | Traffic models | Traffic control | Control theory | Robot dynamics

Journal Article

Journal of Optimization Theory and Applications, ISSN 0022-3239, 9/2017, Volume 174, Issue 3, pp. 785 - 802

In this paper, we discuss a class of fractional optimal control problems, where the system dynamical constraint comprises a combination of classical and...

Fractional optimal control problem | 26A33 | Mathematics | Theory of Computation | Optimization | Fractional derivative | 49M30 | Laguerre polynomials | Calculus of Variations and Optimal Control; Optimization | Operations Research/Decision Theory | Applications of Mathematics | Engineering, general | 49M37 | 49M25 | NUMERICAL SCHEME | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | GENERAL FORMULATION | Analysis | Methods | Algorithms | Control theory | Graphical representations | Nonlinear programming | Quadratic programming | Optimal control

Fractional optimal control problem | 26A33 | Mathematics | Theory of Computation | Optimization | Fractional derivative | 49M30 | Laguerre polynomials | Calculus of Variations and Optimal Control; Optimization | Operations Research/Decision Theory | Applications of Mathematics | Engineering, general | 49M37 | 49M25 | NUMERICAL SCHEME | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | GENERAL FORMULATION | Analysis | Methods | Algorithms | Control theory | Graphical representations | Nonlinear programming | Quadratic programming | Optimal control

Journal Article