scholarly journals Optimal control of nonlinear systems with input constraints using linear time varying approximations

2016 ◽  
Vol 21 (3) ◽  
pp. 400-412 ◽  
Author(s):  
Mehmet Itik
Keyword(s):  
Optimal Control ◽  
Nonlinear Systems ◽  
Optimal Control Problems ◽  
Linear Time ◽  
Input Constraints ◽  
Linear Quadratic ◽  
Constrained Optimal Control ◽  
Linear And Nonlinear ◽  
Bang Bang Control ◽  
Linear And Nonlinear Systems

We propose a new method to solve input constrained optimal control problems for autonomous nonlinear systems affine in control. We then extend the method to compute the bang-bang control solutions under the symmetric control constraints. The most attractive aspect of the proposed technique is that it enables the use of linear quadratic control theory on the input constrained linear and nonlinear systems. We illustrate the effectiveness of our technique both on linear and nonlinear examples and compare our results with those of the literature.

A class of optimal control problems governed by singular systems via Balakrishnan’s method

2020 ◽  
Author(s):  
Abed Makreloufi ◽  
Mohammed Benharrat
Keyword(s):  
Optimal Control ◽  
Optimal Control Problems ◽  
Linear Time ◽  
Singular Systems ◽  
Necessary Optimality Conditions ◽  
Dynamic Mode ◽  
Control Problems ◽  
Differential Algebraic Equation ◽  
Linear Quadratic ◽  
Linear Differential

Abstract The purpose of this paper is to discuss, by the use of the Balakrishnan’s epsilon method, a class of optimal control problems governed by continuous linear time invariant singular systems which have only a finite dynamic mode. The linear differential algebraic equation is handled using the epsilon technique to obtain a sequence of the calculus of variations problems. A convergence theorem is given to obtain approximate and, in the limit, an optimal solution of this class of optimal control problem by the use of the necessary optimality conditions of Euler–Lagrange type. A correspondence has been also shown between this penalty function and duality for this class of optimal control problems considered. As an application, an example of optimal linear quadratic problem is also given.

OPTIMAL CONTROL OF CHAOS IN NONLINEAR DRIVEN OSCILLATORS VIA LINEAR TIME-VARYING APPROXIMATIONS

2008 ◽  
Vol 18 (11) ◽  
pp. 3355-3374 ◽  
Author(s):  
O. HUGUES-SALAS ◽  
S. P. BANKS
Keyword(s):  
Optimal Control ◽  
Nonlinear Systems ◽  
Chaotic Behavior ◽  
Linear Time ◽  
Duffing Oscillator ◽  
Approximation Technique ◽  
Control Procedure ◽  
Time Varying ◽  
Linear Quadratic ◽  
Approximation Sequence

An optimal chaos control procedure is proposed. The aim of using this method is to stabilize the chaotic behavior of forced continuous-time nonlinear systems by using an approximation sequence technique and linear optimal control. The idea of the approximation technique is to use a sequence of linear, time-varying equations to approximate the solution of nonlinear systems. In each of these equations, the linear-quadratic optimal tracking control is applied. The purpose is to find a linear time-varying feedback controller which produces an optimized trajectory that converges to a desired signal. This controller is then used in the original nonlinear system. As an example, the procedure is proved to work in the Duffing oscillator and the chaotic pendulum, in which the goal is to direct chaotic trajectories of these systems to a period-n orbit.

On closed-loop equilibrium strategies for mean-field stochastic linear quadratic problems

2020 ◽  
Vol 26 ◽  
pp. 41
Author(s):  
Tianxiao Wang
Keyword(s):  
Optimal Control ◽  
Closed Loop ◽  
Optimal Control Problems ◽  
Mean Field ◽  
Open Loop ◽  
Time Inconsistency ◽  
Control Problems ◽  
Linear Quadratic ◽  
Linear Quadratic Optimal Control ◽  
Equilibrium Strategies

This article is concerned with linear quadratic optimal control problems of mean-field stochastic differential equations (MF-SDE) with deterministic coefficients. To treat the time inconsistency of the optimal control problems, linear closed-loop equilibrium strategies are introduced and characterized by variational approach. Our developed methodology drops the delicate convergence procedures in Yong [Trans. Amer. Math. Soc. 369 (2017) 5467–5523]. When the MF-SDE reduces to SDE, our Riccati system coincides with the analogue in Yong [Trans. Amer. Math. Soc. 369 (2017) 5467–5523]. However, these two systems are in general different from each other due to the conditional mean-field terms in the MF-SDE. Eventually, the comparisons with pre-committed optimal strategies, open-loop equilibrium strategies are given in details.

Mathematical modeling of conversion of non-Gaussian random processes, signals and noise in linear and nonlinear systems

2018 ◽  
pp. 66-78
Author(s):  
V. M. Artyushenko ◽  
V. I. Volovach
Keyword(s):  
Mathematical Modeling ◽  
Nonlinear Systems ◽  
Random Processes ◽  
Mathematical Transformation ◽  
Positive And Negative Feedback ◽  
Non Linear Systems ◽  
Linear And Nonlinear ◽  
Non Gaussian ◽  
Linear And Nonlinear Systems ◽  
Inertial Systems

The questions connected with mathematical modeling of transformation of non-Gaussian random processes, signals and noise in linear and nonlinear systems are considered and analyzed. The mathematical transformation of random processes in linear inertial systems consisting of both series and parallel connected links, as well as positive and negative feedback is analyzed. The mathematical transformation of random processes with polygamous density of probability distribution during their passage through such systems is considered. Nonlinear inertial and non-linear systems are analyzed.

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