International Journal of Control, ISSN 0020-7179, 10/2017, Volume 90, Issue 10, pp. 2152 - 2164

This paper focuses on the optimal control design for a system of coupled parabolic-hypebolic partial differential equations by using the infinite-dimensional...

linear-quadratic control | eigenvalues problem | hyperbolic PDEs | operator Riccati equation | Optimal control | parabolic PDEs | linear–quadratic control | DISTRIBUTED-PARAMETER SYSTEMS | FEEDBACK-CONTROL | SPECTRAL FACTORIZATION | MODEL-PREDICTIVE CONTROL | AUTOMATION & CONTROL SYSTEMS | Partial differential equations | Computer simulation | Uniqueness | Eigenvalues | Mathematical models | Eigenvectors | Catalysis | Riccati equation

linear-quadratic control | eigenvalues problem | hyperbolic PDEs | operator Riccati equation | Optimal control | parabolic PDEs | linear–quadratic control | DISTRIBUTED-PARAMETER SYSTEMS | FEEDBACK-CONTROL | SPECTRAL FACTORIZATION | MODEL-PREDICTIVE CONTROL | AUTOMATION & CONTROL SYSTEMS | Partial differential equations | Computer simulation | Uniqueness | Eigenvalues | Mathematical models | Eigenvectors | Catalysis | Riccati equation

Journal Article

International Journal of Systems Science, ISSN 0020-7721, 04/2018, Volume 49, Issue 5, pp. 897 - 907

This paper deals with the design of an optimal state-feedback linear-quadratic (LQ) controller for a system of coupled parabolic-hypebolic non-autonomous...

chemical process systems | distributed parameter systems | partial differential equations | time-varying system | Optimal control | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | COMPUTER SCIENCE, THEORY & METHODS | ASYMPTOTIC STABILITY | QUADRATIC CONTROL | AUTOMATION & CONTROL SYSTEMS | Partial differential equations | Computer simulation | State space models | Control systems design | Eigenvalues | Mathematical models | Control stability | Eigenvectors | Catalysis

chemical process systems | distributed parameter systems | partial differential equations | time-varying system | Optimal control | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | COMPUTER SCIENCE, THEORY & METHODS | ASYMPTOTIC STABILITY | QUADRATIC CONTROL | AUTOMATION & CONTROL SYSTEMS | Partial differential equations | Computer simulation | State space models | Control systems design | Eigenvalues | Mathematical models | Control stability | Eigenvectors | Catalysis

Journal Article

Journal of Process Control, ISSN 0959-1524, 09/2015, Volume 33, pp. 102 - 111

•Description and formulation of the coupled parabolic PDE–ODE system of interest.•The eigenvalue problem is solved. Dynamical properties of the model are...

Parabolic PDE | Boundary control | Riesz spectral system | Linear quadratic optimal control | Infinite-dimensional system | ENGINEERING, CHEMICAL | PREDICTIVE CONTROL | AUTOMATION & CONTROL SYSTEMS

Parabolic PDE | Boundary control | Riesz spectral system | Linear quadratic optimal control | Infinite-dimensional system | ENGINEERING, CHEMICAL | PREDICTIVE CONTROL | AUTOMATION & CONTROL SYSTEMS

Journal Article

IEEE Transactions on Automatic Control, ISSN 0018-9286, 04/2017, Volume 62, Issue 4, pp. 1636 - 1651

We present an optimization-based framework for analysis and control of linear parabolic partial differential equations (PDEs) with spatially varying...

Backstepping | Control design | partial differential equations (PDEs) | Observers | Stability analysis | distributed parameter systems | Mathematical model | Numerical stability | Output feedback | Lyapunov methods | sum of squares | HYPERBOLIC SYSTEMS | STABILIZATION | QUADRATIC OPTIMAL-CONTROL | POSED LINEAR-SYSTEMS | ADAPTIVE BOUNDARY CONTROL | AUTOMATION & CONTROL SYSTEMS | ENGINEERING, ELECTRICAL & ELECTRONIC | Usage | Mathematical models | Stability | Research | Differential equations

Backstepping | Control design | partial differential equations (PDEs) | Observers | Stability analysis | distributed parameter systems | Mathematical model | Numerical stability | Output feedback | Lyapunov methods | sum of squares | HYPERBOLIC SYSTEMS | STABILIZATION | QUADRATIC OPTIMAL-CONTROL | POSED LINEAR-SYSTEMS | ADAPTIVE BOUNDARY CONTROL | AUTOMATION & CONTROL SYSTEMS | ENGINEERING, ELECTRICAL & ELECTRONIC | Usage | Mathematical models | Stability | Research | Differential equations

Journal Article

Journal of Differential Equations, ISSN 0022-0396, 11/2019, Volume 267, Issue 10, pp. 5976 - 6003

We consider a non-linear parabolic partial differential equation (PDE) on Rd with a distributional coefficient in the non-linear term. The distribution is an...

Quadratic parabolic PDEs | Singular BSDEs | Singular parabolic PDEs | Distributional coefficients | Besov spaces | MATHEMATICS | SPDES | REGULARITY | DIFFERENTIAL-EQUATIONS | NOISE

Quadratic parabolic PDEs | Singular BSDEs | Singular parabolic PDEs | Distributional coefficients | Besov spaces | MATHEMATICS | SPDES | REGULARITY | DIFFERENTIAL-EQUATIONS | NOISE

Journal Article

SIAM Journal on Control and Optimization, ISSN 0363-0129, 2013, Volume 51, Issue 3, pp. 2442 - 2471

This paper deals with linear-quadratic optimal control problems constrained by a parametric or stochastic elliptic or parabolic partial differential equation...

Distributed or boundary control | Linear parametric or stochastic PDE | Linear-quadratic optimal control | Analyticity | Elliptic or parabolic PDE | Generalized polynomial chaos approximation | MATHEMATICS, APPLIED | distributed or boundary control | TIME | linear parametric or stochastic PDE | EVOLUTION-EQUATIONS | elliptic or parabolic PDE | generalized polynomial chaos approximation | ADAPTIVE WAVELET METHODS | linear-quadratic optimal control | PARTIAL-DIFFERENTIAL-EQUATIONS | FINITE-ELEMENT APPROXIMATIONS | COEFFICIENTS | OPTIMIZATION | DIRICHLET BOUNDARY CONTROL | analyticity | MULTIGRID METHOD | AUTOMATION & CONTROL SYSTEMS | SCHEMES | Tensors | Constraints | Partial differential equations | Mathematical analysis | Mathematical models | Stochasticity | Galerkin methods | Adaptive control systems

Distributed or boundary control | Linear parametric or stochastic PDE | Linear-quadratic optimal control | Analyticity | Elliptic or parabolic PDE | Generalized polynomial chaos approximation | MATHEMATICS, APPLIED | distributed or boundary control | TIME | linear parametric or stochastic PDE | EVOLUTION-EQUATIONS | elliptic or parabolic PDE | generalized polynomial chaos approximation | ADAPTIVE WAVELET METHODS | linear-quadratic optimal control | PARTIAL-DIFFERENTIAL-EQUATIONS | FINITE-ELEMENT APPROXIMATIONS | COEFFICIENTS | OPTIMIZATION | DIRICHLET BOUNDARY CONTROL | analyticity | MULTIGRID METHOD | AUTOMATION & CONTROL SYSTEMS | SCHEMES | Tensors | Constraints | Partial differential equations | Mathematical analysis | Mathematical models | Stochasticity | Galerkin methods | Adaptive control systems

Journal Article

Nonlinear Analysis, ISSN 0362-546X, 01/2016, Volume 131, pp. 273 - 288

In this paper we deal with parabolic problems whose simplest model is {u′−Δpu+B|∇u|pu=0in (0,T)×Ω,u(0,x)=u0(x)in Ω,u(t,x)=0on (0,T)×∂Ω, where T>0, N≥2, p>1,...

Singular parabolic equations | Degenerate parabolic equations | Nonlinear parabolic equations | MATHEMATICS | MATHEMATICS, APPLIED | DATUM | QUADRATIC GRADIENT TERM | Nonlinearity | Mathematical models | Mathematical analysis | Images | Mathematics - Analysis of PDEs

Singular parabolic equations | Degenerate parabolic equations | Nonlinear parabolic equations | MATHEMATICS | MATHEMATICS, APPLIED | DATUM | QUADRATIC GRADIENT TERM | Nonlinearity | Mathematical models | Mathematical analysis | Images | Mathematics - Analysis of PDEs

Journal Article

Applied Mathematics Letters, ISSN 0893-9659, 12/2012, Volume 25, Issue 12, pp. 2184 - 2187

We study several controllability properties for some semilinear parabolic PDE with a quadratic gradient term. For internal distributed controls, it is shown...

Controllability | Quadratic gradient term | MATHEMATICS, APPLIED | HEAT-EQUATION | GROWTH | APPROXIMATE CONTROLLABILITY | NULL-CONTROLLABILITY | Stability | Partial differential equations | Mathematical analysis | Control equipment | Proving | Control systems | Transformations

Controllability | Quadratic gradient term | MATHEMATICS, APPLIED | HEAT-EQUATION | GROWTH | APPROXIMATE CONTROLLABILITY | NULL-CONTROLLABILITY | Stability | Partial differential equations | Mathematical analysis | Control equipment | Proving | Control systems | Transformations

Journal Article

International Journal of Control, ISSN 0020-7179, 2018, pp. 1 - 11

Journal Article

Infinite Dimensional Analysis, Quantum Probability and Related Topics, ISSN 0219-0257, 09/2011, Volume 14, Issue 3, pp. 517 - 536

In this paper, we construct the solutions of semilinear parabolic PDEs with singular coefficients and establish the link to solutions of backward stochastic...

Dirichlet forms | quadratic forms | backward stochastic differential equations | Sobolev solutions | Semilinear parabolic partial differential equations | MATHEMATICS, APPLIED | EQUATIONS | STATISTICS & PROBABILITY | PHYSICS, MATHEMATICAL

Dirichlet forms | quadratic forms | backward stochastic differential equations | Sobolev solutions | Semilinear parabolic partial differential equations | MATHEMATICS, APPLIED | EQUATIONS | STATISTICS & PROBABILITY | PHYSICS, MATHEMATICAL

Journal Article

Numerical Algorithms, ISSN 1017-1398, 07/2017, Volume 75, Issue 3, pp. 699 - 729

We report a new algorithm for solving linear parabolic partial differential equations (PDEs) in one space dimension. The algorithm employs optimal quadratic...

High accuracy | Linear parabolic PDEs | Quadratic spline collocation | Unconditionally stable | Deferred correction | QUADRATIC-SPLINE COLLOCATION | ORDER | MATHEMATICS, APPLIED | TIME | DEFERRED CORRECTION METHODS | Analysis | Algorithms | Differential equations

High accuracy | Linear parabolic PDEs | Quadratic spline collocation | Unconditionally stable | Deferred correction | QUADRATIC-SPLINE COLLOCATION | ORDER | MATHEMATICS, APPLIED | TIME | DEFERRED CORRECTION METHODS | Analysis | Algorithms | Differential equations

Journal Article

Computational Optimization and Applications, ISSN 0926-6003, 3/2006, Volume 33, Issue 2, pp. 209 - 228

This paper addresses the regularization of pointwise state constraints in optimal control problems. By analyzing the associated dual problem, it is shown that...

Convex and Discrete Geometry | Operations Research/Decision Theory | optimal control | Mathematics | pointwise state constraints | Operations Research, Mathematical Programming | Statistics, general | quadratic programming | regular Lagrange multipliers | Optimization | elliptic and parabolic equations | bottleneck constraints | Regular Lagrange multipliers | Pointwise state constraints | Quadratic programming | Bottleneck constraints | Elliptic and parabolic equations | Optimal control | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | PRIMAL-DUAL STRATEGY | Studies | Mathematical models

Convex and Discrete Geometry | Operations Research/Decision Theory | optimal control | Mathematics | pointwise state constraints | Operations Research, Mathematical Programming | Statistics, general | quadratic programming | regular Lagrange multipliers | Optimization | elliptic and parabolic equations | bottleneck constraints | Regular Lagrange multipliers | Pointwise state constraints | Quadratic programming | Bottleneck constraints | Elliptic and parabolic equations | Optimal control | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | PRIMAL-DUAL STRATEGY | Studies | Mathematical models

Journal Article

Inverse Problems and Imaging, ISSN 1930-8337, 2013, Volume 7, Issue 1, pp. 159 - 182

We study the inverse problem of the simultaneous identification of two discontinuous diffusion coefficients for a one-dimensional coupled parabolic system with...

Carleman | Inverse problems | Parabolic system | Quadratic programming | Interior-point method | interior-point method | MATHEMATICS, APPLIED | COEFFICIENTS | parabolic system | PHYSICS, MATHEMATICAL | quadratic programming

Carleman | Inverse problems | Parabolic system | Quadratic programming | Interior-point method | interior-point method | MATHEMATICS, APPLIED | COEFFICIENTS | parabolic system | PHYSICS, MATHEMATICAL | quadratic programming

Journal Article

SIAM Journal on Mathematical Analysis, ISSN 0036-1410, 2013, Volume 45, Issue 3, pp. 1825 - 1870

We study the infinite horizon linear-quadratic (LQ) problem and the associated algebraic Riccati equations for systems with unbounded control actions. The...

Boundary control | Composite partial differential equation systems | Algebraic Riccati equations | Linear quadratic problem | ANALYTICITY | SEMIGROUPS | MATHEMATICS, APPLIED | PARABOLIC-SYSTEMS | NONAUTONOMOUS RICCATI-EQUATIONS | MODELS | linear quadratic problem | composite partial differential equation systems | CLASSICAL-SOLUTIONS | boundary control | algebraic Riccati equations | Algebra | Partial differential equations | Dynamics | Mathematical analysis | Control systems | Mathematical models | Riccati equation

Boundary control | Composite partial differential equation systems | Algebraic Riccati equations | Linear quadratic problem | ANALYTICITY | SEMIGROUPS | MATHEMATICS, APPLIED | PARABOLIC-SYSTEMS | NONAUTONOMOUS RICCATI-EQUATIONS | MODELS | linear quadratic problem | composite partial differential equation systems | CLASSICAL-SOLUTIONS | boundary control | algebraic Riccati equations | Algebra | Partial differential equations | Dynamics | Mathematical analysis | Control systems | Mathematical models | Riccati equation

Journal Article

Journal of Theoretical Probability, ISSN 0894-9840, 12/2010, Volume 23, Issue 4, pp. 951 - 971

This paper has two parts. In part I, the existence and uniqueness are established for Sobolev solutions of a class of semilinear parabolic partial differential...

35D05 | Backward stochastic differential equations | 60H10 | 93E20 | 35R60 | Quadratic growth | Bounded weak solutions | Probability Theory and Stochastic Processes | Mathematics | Statistics, general | 60H30B | Semilinear second-order parabolic equations | STOCHASTIC DIFFERENTIAL-EQUATIONS | REFLECTED BSDE | SPDES | OBSTACLE | STATISTICS & PROBABILITY

35D05 | Backward stochastic differential equations | 60H10 | 93E20 | 35R60 | Quadratic growth | Bounded weak solutions | Probability Theory and Stochastic Processes | Mathematics | Statistics, general | 60H30B | Semilinear second-order parabolic equations | STOCHASTIC DIFFERENTIAL-EQUATIONS | REFLECTED BSDE | SPDES | OBSTACLE | STATISTICS & PROBABILITY

Journal Article

SIAM Journal on Control and Optimization, ISSN 0363-0129, 2006, Volume 45, Issue 1, pp. 74 - 106

In this paper, we prove a comparison result between semicontinuous viscosity sub- and supersolutions growing at most quadratically of second-order degenerate...

Linear quadratic problems | Nonlinear Isaacs equations | Degenerate parabolic equations | Maximum principle | Nonlinear Hamilton-Jacobi equations | Unbounded solutions | Viscosity solutions | MATHEMATICS, APPLIED | PARABOLIC EQUATIONS | DIFFUSION-PROCESSES | Jacobi equations | nonlinear Isaacs equations | HAMILTON-JACOBI EQUATIONS | PRINCIPLE | maximum principle | nonlinear Hamilton | degenerate parabolic equations | unbounded solutions | RISK-SENSITIVE CONTROL | FINITE-TIME-HORIZON | PARTIAL-DIFFERENTIAL-EQUATIONS | linear quadratic problems | SYSTEMS | viscosity solutions | AUTOMATION & CONTROL SYSTEMS | Mathematics - Analysis of PDEs | Analysis of PDEs | Mathematics

Linear quadratic problems | Nonlinear Isaacs equations | Degenerate parabolic equations | Maximum principle | Nonlinear Hamilton-Jacobi equations | Unbounded solutions | Viscosity solutions | MATHEMATICS, APPLIED | PARABOLIC EQUATIONS | DIFFUSION-PROCESSES | Jacobi equations | nonlinear Isaacs equations | HAMILTON-JACOBI EQUATIONS | PRINCIPLE | maximum principle | nonlinear Hamilton | degenerate parabolic equations | unbounded solutions | RISK-SENSITIVE CONTROL | FINITE-TIME-HORIZON | PARTIAL-DIFFERENTIAL-EQUATIONS | linear quadratic problems | SYSTEMS | viscosity solutions | AUTOMATION & CONTROL SYSTEMS | Mathematics - Analysis of PDEs | Analysis of PDEs | Mathematics

Journal Article

IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics), ISSN 1083-4419, 06/2012, Volume 42, Issue 3, pp. 927 - 938

In this paper, a distributed fuzzy control design based on Proportional-spatial Derivative (P-sD) is proposed for the exponential stabilization of a class of...

Algorithm design and analysis | Fuzzy control | State feedback | Symmetric matrices | Control design | spatially distributed systems (SDSs) | Mathematical model | Exponential stability | linear matrix inequalities (LMIs) | Takagi-Sugeno (T-S) fuzzy model | Equations | fuzzy control | CONTROL DESIGN | DELAYS | STABILIZATION CONDITIONS | COMPUTER SCIENCE, CYBERNETICS | REACTOR | PARAMETER-SYSTEMS | TRACKING | OBSERVER-BASED CONTROL | Models, Theoretical | Algorithms | Feedback | Artificial Intelligence | Computer Simulation | Decision Support Techniques | Nonlinear Dynamics | Fuzzy Logic | Pattern Recognition, Automated - methods | Fuzzy logic | Technology application | Usage | Perturbation (Mathematics) | Equations, Quadratic | Innovations | Fuzzy algorithms | Distributed processing (Computers) | Differential equations, Partial | Fuzzy systems

Algorithm design and analysis | Fuzzy control | State feedback | Symmetric matrices | Control design | spatially distributed systems (SDSs) | Mathematical model | Exponential stability | linear matrix inequalities (LMIs) | Takagi-Sugeno (T-S) fuzzy model | Equations | fuzzy control | CONTROL DESIGN | DELAYS | STABILIZATION CONDITIONS | COMPUTER SCIENCE, CYBERNETICS | REACTOR | PARAMETER-SYSTEMS | TRACKING | OBSERVER-BASED CONTROL | Models, Theoretical | Algorithms | Feedback | Artificial Intelligence | Computer Simulation | Decision Support Techniques | Nonlinear Dynamics | Fuzzy Logic | Pattern Recognition, Automated - methods | Fuzzy logic | Technology application | Usage | Perturbation (Mathematics) | Equations, Quadratic | Innovations | Fuzzy algorithms | Distributed processing (Computers) | Differential equations, Partial | Fuzzy systems

Journal Article

Numerical Algorithms, ISSN 1017-1398, 4/2010, Volume 53, Issue 4, pp. 511 - 553

New methods for solving general linear parabolic partial differential equations (PDEs) in one space dimension are developed. The methods combine...

Stability | Numeric Computing | Theory of Computation | Optimal order of convergence | Parabolic PDEs | Crank-Nicolson | Algebra | Algorithms | Collocation | Computer Science | Mathematics, general | Quadratic splines | American options | MATHEMATICS, APPLIED | PDES | Computer science | Mathematical optimization | Analysis | Pricing | Linear systems | Discretization | Partial differential equations | Mathematical analysis | Mathematical models | Convergence

Stability | Numeric Computing | Theory of Computation | Optimal order of convergence | Parabolic PDEs | Crank-Nicolson | Algebra | Algorithms | Collocation | Computer Science | Mathematics, general | Quadratic splines | American options | MATHEMATICS, APPLIED | PDES | Computer science | Mathematical optimization | Analysis | Pricing | Linear systems | Discretization | Partial differential equations | Mathematical analysis | Mathematical models | Convergence

Journal Article

Milan Journal of Mathematics, ISSN 1424-9286, 12/2010, Volume 78, Issue 2, pp. 417 - 455

The goal of this paper is to describe the state of the art on the question of global existence of solutions to reaction-diffusion systems for which two main...

nonlinear diffusion | Primary 3502 | blow up | Mathematics | 35K57 | Lotka-Volterra | 92E20 | global existence | chemical kinetics | combustion | Analysis | Reaction-diffusion | Secondary 92C45 | Mathematics, general | semilinear systems | quadratic systems | parabolic equations | DISSIPATION | MATHEMATICS, APPLIED | SEMILINEAR PARABOLIC-SYSTEMS | DECAY | EQUATIONS | BOUNDEDNESS | MATHEMATICS | BOUNDS | GROWTH | BLOWUP | Analysis of PDEs

nonlinear diffusion | Primary 3502 | blow up | Mathematics | 35K57 | Lotka-Volterra | 92E20 | global existence | chemical kinetics | combustion | Analysis | Reaction-diffusion | Secondary 92C45 | Mathematics, general | semilinear systems | quadratic systems | parabolic equations | DISSIPATION | MATHEMATICS, APPLIED | SEMILINEAR PARABOLIC-SYSTEMS | DECAY | EQUATIONS | BOUNDEDNESS | MATHEMATICS | BOUNDS | GROWTH | BLOWUP | Analysis of PDEs

Journal Article

Journal of Process Control, ISSN 0959-1524, 11/2018, Volume 71, pp. 63 - 74

•The SCR dynamics and its mathematical representation have been described.•An approximation technique for the computation of the eigenvalues and eigenvectors...

Linear quadratic optimal control | Diesel engines | Boundary system control | Hyperbolic PDEs | Selective catalytic reduction | Distributed parameter systems | Parabolic PDEs | ENGINEERING, CHEMICAL | AUTOMATION & CONTROL SYSTEMS | Ammonia | Control systems | Algorithms | Numerical analysis | Diesel motor | Analysis

Linear quadratic optimal control | Diesel engines | Boundary system control | Hyperbolic PDEs | Selective catalytic reduction | Distributed parameter systems | Parabolic PDEs | ENGINEERING, CHEMICAL | AUTOMATION & CONTROL SYSTEMS | Ammonia | Control systems | Algorithms | Numerical analysis | Diesel motor | Analysis

Journal Article

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