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Semidefinite Relaxations for Stochastic Optimal Control Policies
[article]
2014
arXiv
pre-print
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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
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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
2008
Applied Mathematics and Computation
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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
2008
IEEE Transactions on Neural Networks
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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
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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
2008
Applied Mathematics and Optimization
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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
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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
2012
Automatica
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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
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., +, 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
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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)
2006
Industrial & Engineering Chemistry Research
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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]
1996
Control and Dynamic Systems
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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]
2014
arXiv
pre-print
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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
2016
IFAC-PapersOnLine
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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
2018
Automatica
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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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