Formal Controller Synthesis via Genetic Programming

Abstract

This paper proposes a framework for automatic formal controller synthesis for general hybrid systems with a subset of safety and reachability specifications. The framework uses genetic programming to automatically co-synthesize controllers and candidate Lyapunov-like functions. These candidate Lyapunov-like functions are used to formally verify the control specification, and their correctness is proven using a Satisfiability Modulo Theories solver. The advantages of this approach are: no restriction is made to polynomial systems, the synthesized controllers are expressed as compact expressions, and no explicit solution structure has to be specified beforehand. We demonstrate the effectiveness of the proposed framework in several case studies, including nonpolynomial systems, sampled-data systems, systems with bounded uncertainties, switched systems, and systems with jumps.

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

“…Remark 2. Comparing the CLBF for RSWS to the CLBF in [15], in this work the condition on the derivative of V is only imposed for the sublevel set A ⊂ S, rather than the entire safe set S. Secondly, the CLBF in this work involves only 2 parameters y and β, as opposed to 5 in [15].…”

“…This work is a follow-up to [15], in which also a combination of GP and SMT solvers is used. The main contributions of this paper are: 1) synthesis w.r.t.…”

“…Furthermore, this paper extends the set of specifications to include invariance of the goal set. Finally, similar to [15], the theoretical lower bounds on the minimum dwell-times reported in [16] are often very conservative.…”

Optimal Symbolic Controllers Determinization for BDD storage

“…In this work, similar to [30], we employ grammar guided genetic programming algorithms (GGGP) to find multi-dimensional analytical expressions fitting the controller's data. In fact, the genetic process follows [29] except for that the realvalue parameter tuning is done with CMA-ES [10]. To speed up the CMA-ES procedure, we use sep-CMA-ES which has a linear time and space complexity [21].…”

“…The reproduction involves selecting individuals based on tournament selection and the genetic operators crossover and mutation, in which parts of the individuals are exchanged or randomly altered respectively. More in depth descriptions of the used GGGP and sep-CMA-ES algorithms can be found in [29] and [21] respectively. After a maximum amount of generations the individual with the highest fitness is selected.…”