Formal Synthesis of Analytic Controllers for Sampled-Data Systems via Genetic Programming

Abstract

This paper presents an automatic formal controller synthesis method for nonlinear sampled-data systems with safety and reachability specifications. Fundamentally, the presented method is not restricted to polynomial systems and controllers. We consider periodically switched controllers based on a Control Lyapunov Barrier-like functions. The proposed method utilizes genetic programming to synthesize these functions as well as the controller modes. Correctness of the controller are subsequently verified by means of a Satisfiability Modulo Theories solver. Effectiveness of the proposed methodology is demonstrated on multiple systems.

Formal Controller Synthesis via Genetic Programming

“…Moreover, in our benchmarks we synthesize sampled-data controllers with a larger sampling time than the minimum dwell-times presented in [33,49]. Finally, we are not able to find sampled-data controllers for all systems in Table 1 (systems 3 and 4) as opposed to our previous work [38]. In the case of system 3, this is due to time-out issues with the SMT solver as a result of the increased complexity w.r.t.…”

“…Given an individual, a metric on how well the objective is achieved is captured in a fitness function. The algorithm is initialized with a randomly generated We use grammar-guided genetic programming (GGGP) [38,39], which imposes that the genotype adheres to a certain grammar in Backus-Naur form (BNF) [54]. The BNF grammar is defined by the tuple (N , S, P), where N denotes a set of nonterminals, S ∈ N is a starting tree, and P are the production rules.…”

“…with D s = ∅. We consider five systems, adopted from [38] and references therein, defined by the open-loop continuous dynamics f ol,x : R nx × U → R nx shown in Table 1. These systems are: a linear system, 2nd-and 3rd-order polynomial systems, a pendulum system, and a pendulum-on-cart system.…”

“…Taking inspiration from synthesis of switching controllers based on a CLFB (see e.g. [33], [38]), the controller is based on the candidate LBF V , In other words, a mode q is selected so that it minimizes ∇V (s), f q (s) . This is achieved by the following controller:…”

“…a fixed-order polynomial. We use a variant of grammar guided genetic programming (GGGP) [37,38], which employs grammars to constrain the search space. The ability to automatically adapt and modify the solution structures is particularly useful when no solution exists for a certain parametrization, as the algorithm explores other structures automatically.…”