Abstract
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.
Highlights
Control of nonlinear systems is of great importance since many systems have inherent nonlinearities
Optimal control problems whose solutions are of bang-bang, are solved by using indirect shooting methods to solve the multi-point boundary value problem obtained from the c Vilnius University, 2016
We show that using the input constrained theory, one can obtain near minimum-time bangbang type control solutions for both linear and nonlinear systems without any requirement of the knowledge for the initial value of the control input and the number of bang-bang switchings since they are directly obtained from the solutions of the differential Riccati equations for the approximate linear time-varying systems
Summary
Control of nonlinear systems is of great importance since many systems have inherent nonlinearities. Solving these problems is extremely difficult since very good initial guesses for switching arc durations and the values of the states at the switching instants are required Direct optimization methods, such as nonlinear programming, can be used to find bang-bang control solutions for nonlinear systems. Input constrained control of nonlinear systems are studied by using a special kind of approximation technique In this method, the nonlinear system is represented in the form of a series of linear time-varying (LTV) systems whose responses converge to the nonlinear system’s response in the limit. We show that using the input constrained theory, one can obtain near minimum-time bangbang type control solutions for both linear and nonlinear systems without any requirement of the knowledge for the initial value of the control input and the number of bang-bang switchings since they are directly obtained from the solutions of the differential Riccati equations for the approximate linear time-varying systems.
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