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This paper presents a safe robust policy iteration (SR-PI) algorithm todesign controllers with satisficing (good enough) performance and safetyguarantee. This is in contrast to standard PI-based control design methods withno safety certification. It also moves away from existing safe control designapproaches that perform pointwise optimization and are thus myopic. Safetyassurance requires satisfying a control barrier function (CBF), which might bein conflict with the performance-driven Lyapunov solution to the Bellmanequation arising in each iteration of the PI. Therefore, a new development isrequired to robustly certify the safety of an improved policy at each iterationof the PI. The proposed SR-PI algorithm unifies performance guarantee (providedby a Bellman inequality) with safety guarantee (provided by a robust CBF) ateach iteration. The Bellman inequality resembles the satisficing decisionmaking framework and parameterizes the sacrifice on the performance with anaspiration level when there is a conflict with safety. This aspiration level isoptimized at each iteration to minimize the sacrifice on the performance. It isshown that the presented satisficing control policies obtained at eachiteration of the SR-PI guarantees robust safety and performance. Robuststability is also guaranteed when there is no conflict with safety. Sum ofsquares (SOS) program is employed to implement the proposed SR-PI algorithmiteratively. Finally, numerical simulations are carried out to illustrate theproposed satisficing control framework.

A Satisficing Control Design Framework with Safety and Performance Guarantees for Constrained Systems under Disturbances