Primal-dual method for solving a linear-quadratic multi-input optimal control problem

2019 ◽  
Vol 14 (3) ◽  
pp. 653-669 ◽  
Author(s):  
Noureddine Khimoum ◽  
Mohand Ouamer Bibi
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Dual Method ◽  
Linear Quadratic ◽  
Primal Dual

The linear quadratic optimal control problem for discrete-time Markov jump linear singular systems

Automatica ◽  
2021 ◽  
Vol 127 ◽  
pp. 109506
Author(s):  
Jorge R. Chávez-Fuentes ◽  
Eduardo F. Costa ◽  
Marco H. Terra ◽  
Kaio D.T. Rocha
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Discrete Time ◽  
Singular Systems ◽  
Linear Quadratic ◽  
Markov Jump ◽  
Linear Quadratic Optimal Control ◽  
Quadratic Optimal Control

scholarly journals Convergence results for an averaged LQR problem with applications to reinforcement learning

2021 ◽  
Author(s):  
Andrea Pesare ◽  
Michele Palladino ◽  
Maurizio Falcone
Keyword(s):  
Optimal Control ◽  
Reinforcement Learning ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Current System ◽  
Numerical Test ◽  
Linear Quadratic ◽  
Linear Quadratic Optimal Control ◽  
Lqr Problem ◽  
Quadratic Optimal Control

AbstractIn this paper, we will deal with a linear quadratic optimal control problem with unknown dynamics. As a modeling assumption, we will suppose that the knowledge that an agent has on the current system is represented by a probability distribution $$\pi $$ π on the space of matrices. Furthermore, we will assume that such a probability measure is opportunely updated to take into account the increased experience that the agent obtains while exploring the environment, approximating with increasing accuracy the underlying dynamics. Under these assumptions, we will show that the optimal control obtained by solving the “average” linear quadratic optimal control problem with respect to a certain $$\pi $$ π converges to the optimal control driven related to the linear quadratic optimal control problem governed by the actual, underlying dynamics. This approach is closely related to model-based reinforcement learning algorithms where prior and posterior probability distributions describing the knowledge on the uncertain system are recursively updated. In the last section, we will show a numerical test that confirms the theoretical results.

scholarly journals Two Inverse Problems Solution by Feedback Tracking Control

Axioms ◽  
2021 ◽  
Vol 10 (3) ◽  
pp. 137
Author(s):  
Vladimir Turetsky
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Feedback Linearization ◽  
Linear Quadratic ◽  
Linear Quadratic Optimal Control ◽  
Linear Quadratic Tracking ◽  
Ill Posed ◽  
Quadratic Optimal Control ◽  
Quadratic Tracking

Two inverse ill-posed problems are considered. The first problem is an input restoration of a linear system. The second one is a restoration of time-dependent coefficients of a linear ordinary differential equation. Both problems are reformulated as auxiliary optimal control problems with regularizing cost functional. For the coefficients restoration problem, two control models are proposed. In the first model, the control coefficients are approximated by the output and the estimates of its derivatives. This model yields an approximating linear-quadratic optimal control problem having a known explicit solution. The derivatives are also obtained as auxiliary linear-quadratic tracking controls. The second control model is accurate and leads to a bilinear-quadratic optimal control problem. The latter is tackled in two ways: by an iterative procedure and by a feedback linearization. Simulation results show that a bilinear model provides more accurate coefficients estimates.

Linear quadratic Pareto optimal control problem of stochastic singular systems

2017 ◽  
Vol 354 (2) ◽  
pp. 1220-1238 ◽  
Author(s):  
Weihai Zhang ◽  
Yaning Lin ◽  
Lingrong Xue
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Singular Systems ◽  
Pareto Optimal ◽  
Linear Quadratic ◽  
Stochastic Singular Systems

scholarly journals Maximum Principle for Stochastic Recursive Optimal Control Problems Involving Impulse Controls

2012 ◽  
Vol 2012 ◽  
pp. 1-16 ◽  
Author(s):  
Zhen Wu ◽  
Feng Zhang
Keyword(s):  
Optimal Control ◽  
Maximum Principle ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Optimality Conditions ◽  
Control Variable ◽  
Necessary Optimality Conditions ◽  
Sufficient Optimality Conditions ◽  
Linear Quadratic ◽  
Regular Control

We consider a stochastic recursive optimal control problem in which the control variable has two components: the regular control and the impulse control. The control variable does not enter the diffusion coefficient, and the domain of the regular controls is not necessarily convex. We establish necessary optimality conditions, of the Pontryagin maximum principle type, for this stochastic optimal control problem. Sufficient optimality conditions are also given. The optimal control is obtained for an example of linear quadratic optimization problem to illustrate the applications of the theoretical results.

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