Optimal Feedback Control for Stochastic Impulsive Linear Systems Subject to Poisson Processes

Abstract

This chapter considers a class of optimal feedback control problems, where its dynamical system is described by stochastic linear systems subject to Poisson processes and with state jumps. We show that this stochastic impulsive optimal parameter selection problem is equivalent to a deterministic impulsive optimal parameter selection problem, where the times at which the jumps occurred as well as their heights are decision variables. Then, by introducing a time scaling transform, we show that this deterministic impulsive optimal parameter selection problem is transformed into an equivalent deterministic impulsive optimal parameter selection problem with fixed jump times. For the numerical computation, we derive the gradient formulae of the cost function and the constraint functions. On this basis, an efficient computational method is developed and an example is solved for illustration.