Maximum Principle and Turnpike Properties for Systems with Random Modal Jumps
This chapter deals with a class of stochastic control systems where the random disturbances are stochastic jump processes taking values in a finite set E. Each value i ∈ E can be interpreted as a “mode” of the dynamic system. Systems with modal disturbances have been studied in the control literature for a long time in particular in the case of linear dynamics and quadratic performance criterion (e.g. ). Here we demonstrate that these processes may be viewed as a sequence of control problems with random stopping time. Each of these problems can be rewritten as a deterministic infinite horizon control system with state and control dependent discount rate. Exploiting this property we first extend the infinite horizon Maximum Principle and some turnpike properties from Chapter 6 to the class of control problems with random stopping time. We conclude by applying these turnpike properties to the case of control systems with random modal jumps.
KeywordsHamiltonian System Optimal Control Problem Preventive Maintenance Admissible Pair Infinite Horizon
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