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Semidefinite Relaxations for Stochastic Optimal Control Policies [article]

Matanya B. Horowitz, Joel W. Burdick
2014 arXiv   pre-print
This work proposes a new method obtaining approximate solutions to these linear stochastic optimal control (SOC) problems.  ...  Recent results in the study of the Hamilton Jacobi Bellman (HJB) equation have led to the discovery of a formulation of the value function as a linear Partial Differential Equation (PDE) for stochastic  ...  This work was partially supported by DARPA, through the ARM-S and DRC programs, as well as the Robotics Technology Consortium Alliance (RCTA).  ... 
arXiv:1402.2763v1 fatcat:mdq5v63kfjdgrnhmefvdw6sj5m

2020 Index IEEE Transactions on Automatic Control Vol. 65

2020 IEEE Transactions on Automatic Control  
Fredholm Backstepping Control of Coupled Linear Parabolic PDEs With Input and Output Delays.  ...  ., +, TAC March 2020 909-924 Fredholm Backstepping Control of Coupled Linear Parabolic PDEs With Input and Output Delays.  ...  Linear programming A Decentralized Event-Based Approach for Robust Model Predictive Control.  ... 
doi:10.1109/tac.2020.3046985 fatcat:hfiqhyr7sffqtewdmcwzsrugva

Suboptimal minimax design of constrained parabolic systems with mixed boundary control

Boris Mordukhovich
2008 Applied Mathematics and Computation  
The paper concerns minimax control problems for linear multidimensional parabolic systems with distributed uncertain perturbations and control functions acting in mixed (Robin) boundary conditions.  ...  \Sily implemented suboptimal structure of the feedback boundary regulator and compute its optimal •parameters ensuring the required state performance and robust stability of the nonlinear closed-loop control  ...  The system dynamics is given by the multidimensional linear parabolic equation where !1 C IR" is a bounded domain with the closure cJ !1 and the boundary 8!  ... 
doi:10.1016/j.amc.2008.05.036 fatcat:d2o5zmxnxzaabj4kbeibymrewq

A Galerkin/Neural-Network-Based Design of Guaranteed Cost Control for Nonlinear Distributed Parameter Systems

Huai-Ning Wu, Han-Xiong Li
2008 IEEE Transactions on Neural Networks  
describes the dynamics of the dominant (slow) modes of the PDE system.  ...  This paper presents a Galerkin/neural-networkbased guaranteed cost control (GCC) design for a class of parabolic partial differential equation (PDE) systems with unknown nonlinearities.  ...  In [1] , [3] - [6] , the finite-dimensional control problems of linear parabolic PDE systems were studied. To overcome the problem of high dimensionality, Christofides et al.  ... 
doi:10.1109/tnn.2007.912592 pmid:18467209 fatcat:krrz4twi4ra3zdqxerz5nisyli

Page 2054 of Mathematical Reviews Vol. , Issue 97C [page]

1997 Mathematical Reviews  
Maksimov], Some dynamical inverse problems for hyperbolic systems (465-481); Piermarco Cannarsa and Maria Elisabetta Tessitore, Dynamic programming equation for a class of non- linear boundary control  ...  Kha- palov], On unique continuation of solutions of the parabolic equation from a curve (451-463); Vyacheslav I. Maksimov [V. 1.  ... 

On Aronsson Equation and Deterministic Optimal Control

Pierpaolo Soravia
2008 Applied Mathematics and Optimization  
The methodology uses a Piecewise Linear (PWL) approximation of the Ordinary Differential Equations (ODEs) vector field which describes the dynamics of a system parameterized by the control inputs in order  ...  A measure of the dynamics approximation error is used to estimate upper and lower bounds for the error between the actual and the approximated trajectories once the control vector calculated with the PWL  ...  MS2 Suboptimal Feedback Control Design of Constrained Parabolic Systems in Uncertainty Conditions The talk concerns minimax control problems for linear parabolic systems with uncertain perturbations  ... 
doi:10.1007/s00245-008-9048-7 fatcat:kihxqtczfzdn5pbmvsd42axbk4

Distributed Optimal Control of Multiscale Dynamical Systems: A Tutorial

2016 IEEE Control Systems  
She is the director of the Laboratory for Intelligent Systems and Controls, and her principal research interests include robust adaptive control of aircraft, learning and approximate dynamic programming  ...  His research interests include approximate dynamic programming, optimal control of mobile sensor networks, signal processing, machine learning, and neural networks. He is a Member of the IEEE.  ...  In CINT, the PDE solution is approximated by a linear combination of polynomial basis functions used to satisfy the PDE operator and Gaussian or radial basis functions used to enforce the boundary conditions  ... 
doi:10.1109/mcs.2015.2512034 fatcat:gks3a2r2ejhptkzu7ngjlbgsgy

Boundary second-order sliding-mode control of an uncertain heat process with unbounded matched perturbation

Alessandro Pisano, Yury Orlov
2012 Automatica  
The underlying heat process is governed by an uncertain parabolic partial differential equation (PDE) with Neumann boundary conditions.  ...  The primary concern of the present paper is the regulation of an uncertain heat process with collocated boundary sensing and actuation.  ...  In this paper we address the boundary control problem for an uncertain heat process, governed by a parabolic PDE with a scalar spatial variable ξ ∈ [0, 1] and with Neumann boundary conditions (BC's).  ... 
doi:10.1016/j.automatica.2012.05.041 fatcat:2ztwm56rhvboflvncig6lwdrvq

2018 Index IEEE Transactions on Automatic Control Vol. 63

2018 IEEE Transactions on Automatic Control  
., +, TAC Jan. 2018 117-131 PDE Boundary Control of Multi-Input LTI Systems With Distinct and Uncertain Input Delays.  ...  ., TAC Sept. 2018 3105-3111 PDE Boundary Control of Multi-Input LTI Systems With Distinct and Uncertain Input Delays.  ... 
doi:10.1109/tac.2019.2896796 fatcat:bwmqasulnzbwhin5hv4547ypfe

Page 6770 of Mathematical Reviews Vol. , Issue 96k [page]

1996 Mathematical Reviews  
Chapter 1. Optimization of linear sys- tems. Chapter 2. Dynamic uncertain systems. Chapter 3. Optimal controllers. Chapter 4. Constructing optimal feedback controls. Appendix.  ...  This procedure is based on adaptation of the dual methods of linear programming to opti- mization of dynamic systems.  ... 

Predictive Output Feedback Control of Parabolic Partial Differential Equations (PDEs)

Stevan Dubljevic, Panagiotis D. Christofides
2006 Industrial & Engineering Chemistry Research  
The controllers are applied to an example of a linear parabolic PDE with Dirichlet boundary conditions subject to state and control constraints, and the numerical simulations demonstrate their ability  ...  This work focuses on predictive output feedback control of linear parabolic partial differential equation (PDE) systems with state and control constraints.  ...  To provide a PDE example that belongs in this class of infinite-dimensional systems, we begin by focusing on a linear parabolic PDE with distributed control of the form with the following boundary and  ... 
doi:10.1021/ie0510425 fatcat:jvizjz22wzbevns4dmnalilx6e

Techniques in Computational Stochastic Dynamic Programming [chapter]

Floyd B. Hanson
1996 Control and Dynamic Systems  
Hence, there is a great need to develop the use of high performance computing techniques in stochastic dynamic programming for direct solutions of stochastic optimal control problems.  ...  Quadrat and coworkers [1] have made applications to the control of electric power systems. One emphasis here is the use high performance computing techniques on a wider range of applications.  ...  Now, substituting the control linear dynamics, quadratics costs model (6,13, that models the behavior of the original nonlinear stochastic dynamical programming PDE.  ... 
doi:10.1016/s0090-5267(96)80017-x fatcat:7mtk4gtcmfhippn72sjnnox5ke

A Convex Approach to Output Feedback Control of Parabolic PDEs Using Sum-of-Squares [article]

Aditya Gahlawat, Matthew. M. Peet
2014 arXiv   pre-print
In this paper we use optimization-based methods to design output-feedback controllers for a class of one-dimensional parabolic partial differential equations.  ...  We then show how feasibility of these LOIs may be tested using Semidefinite Programming (SDP) and the Sum-of-Squares methodology.  ...  Acknowledgements This research was carried out with the financial support of the Chateaubriand fellowship program and NSF CAREER Grant CMMI-1151018.  ... 
arXiv:1408.5206v1 fatcat:f4gqfjxoynhzrg6wrc7g357kiu

Interval observers for PDEs: approximation approach

Tatiana Kharkovskaia, Denis Efimov, Andrey Polyakov, Jean-Pierre Richard
2016 IFAC-PapersOnLine  
The problem of interval state estimation is studied for systems described by parabolic Partial Differential Equations (PDEs).  ...  The proposed solution is based on a finite-element approximation of PDE, with posterior design of an interval observer for the obtained ordinary differential equation.  ...  For future research, the proposed interval observer can be used for control design of an uncertain PDE system in the spirit of Efimov et al. (2013) .  ... 
doi:10.1016/j.ifacol.2016.10.283 fatcat:fqwq667chnerdpxkn3pbsaar6u

Design of interval observers and controls for PDEs using finite-element approximations

Tatiana Kharkovskaya, Denis Efimov, Andrey Polyakov, Jean-Pierre Richard
2018 Automatica  
Finally, the obtained interval estimates are used to design a dynamic output stabilizing control.  ...  Second, the interval inclusion of the state function of the PDE is calculated using the error estimates of the finite-element approximation.  ...  The decomposition basis Conclusion Taking a parabolic PDE with Dirichlet boundary conditions, a method of design of interval observers is proposed, which is based on a finite-element approximation.  ... 
doi:10.1016/j.automatica.2018.03.016 fatcat:3jdx7s2hpvez3dajpmfg4vhrdm
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