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Originating in the artificial intelligence literature, optimistic planning(OP) is an algorithm that generates near-optimal control inputs for genericnonlinear discrete-time systems whose input set is finite. This technique istherefore relevant for the near-optimal control of nonlinear switched systems,for which the switching signal is the control. However, OP exhibits severallimitations, which prevent its application in a standard control context.First, it requires the stage cost to take values in [0,1], an unnaturalprerequisite as it excludes, for instance, quadratic stage costs. Second, itrequires the cost function to be discounted. Third, it applies for rewardmaximization, and not cost minimization. In this paper, we modify OP toovercome these limitations, and we call the new algorithm OPmin. We then makestabilizability and detectability assumptions, under which we derivenear-optimality guarantees for OPmin and we show that the obtained bound hasmajor advantages compared to the bound originally given by OP. In addition, weprove that a system whose inputs are generated by OPmin in a receding-horizonfashion exhibits stability properties. As a result, OPmin provides a new toolfor the near-optimal, stable control of nonlinear switched discrete-timesystems for generic cost functions.

Optimistic planning for the near-optimal control of nonlinear switched discrete-time systems with stability guarantees