Symbolic solution of non-Markovian jump linear quadratic (JLQ) systems

The authors consider a class of scalar JLQ problems wherein the form transition probabilities are state-dependent and are piecewise constant in the state. The optimal solution is known to exhibit interesting algorithmic formulations of the control involving logical expressions and recursions. These are amenable to symbolic computation rather than to numerical processing. Symbolic computational methods can be used to design the optimal control law explicitly. A specific example is given, and extensions to more general problems are discussed