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.
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