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.

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.

scholarly journals On the existence of a solution for some distributed optimal control hyperbolic system

2000 ◽  
Vol 23 (5) ◽  
pp. 297-311 ◽  
Author(s):  
Dariusz Idczak ◽  
Stanislaw Walczak
Keyword(s):  
Optimal Control ◽  
Hyperbolic System ◽  
Convex Set ◽  
Linear Time ◽  
Time Varying ◽  
Optimal Process ◽  
Existence Of A Solution ◽  
Distributed Optimal Control ◽  
Absolutely Continuous ◽  
State Variable

We consider a Bolza problem governed by a linear time-varying Darboux-Goursat system and a nonlinear cost functional, without the assumption of the convexity of an integrand with respect to the state variable. We prove a theorem on the existence of an optimal process in the classes of absolutely continuous trajectories of two variables and measurable controls with values in a fixed compact and convex set.

Existence of Solutions of Riccati Differential Equations

2012 ◽  
Vol 134 (3) ◽  
Author(s):  
Sinan Kilicaslan ◽  
Stephen P. Banks
Keyword(s):  
Differential Equation ◽  
Nonlinear Systems ◽  
Existence Of Solutions ◽  
Linear Time ◽  
Sufficient Conditions ◽  
Necessary Condition ◽  
Time Varying ◽  
Riccati Differential Equation ◽  
Riccati Differential Equations ◽  
Time Varying Systems

A necessary condition for the existence of the solution of the Riccati differential equation for both linear, time varying systems and nonlinear systems is introduced. First, a necessary condition for the existence of the solution of the Riccati differential equation for linear, time varying systems is proposed. Then, the sufficient conditions to satisfy the necessary condition are given. After that, the existence of the solution of the Riccati differential equation is generalized for nonlinear systems.

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