Hybrid Optimal Control Synthesis By Classification-based Derivative-free Optimization

Hybrid systems are dynamical systems that combine the domain knowledge of computer science and control theory.Both discrete transitions and continuous changes are involved in the hybrid system,therefore,the behavior of such systems can be quite complex.A hybrid system contains multiple control modes and various continuous variables.The system can switch between different modes.Meanwhile,its variables change continuously according to the differential equations in each control mode.Over the past two decades,hybrid systems have been widely used in various areas such as industry,transportation,biological systems,and so on.The hybrid optimal control synthesis problem is one of the most important problems in the safety-critical study area of hybrid systems.The above synthesis problem attempts to generate a sequence of control modes of the HA model of the system and also generate the corresponding dwell time and control inputs in each control mode to meet some specific control target.However,due to the complex behavior of hybrid systems and a large number of constraints,including combination constraints and continuous constraints,the optimal control synthesis problem of such systems is difficult.Traditional works can generate numerical solutions but they require the objective function and constraints to be differentiable.While non-differentiable behavior such as piece-wise control functions widely exists in hybrid systems and it cannot be solved by existing works.In this paper,we propose a practical and efficient method to solve a general class of hybrid optimal control problems.Our contributions include:?We propose a new hybrid optimal control synthesis framework based on the derivativefree optimization methods,which can solve general hybrid optimal synthesis problems without any limitations.At the discrete level,we traverse the HA model of the system as a directed graph and enumerate all the candidate control mode sequences.At the continuous level,we transform the synthesis problem of the dwell time and control inputs in each mode to a minimization problem by designing penalty functions to encode all the constraints.Then,we give a classification-based derivativefree optimization method to solve the above minimization problem.The experiments on the vehicle and drone control problems demonstrate the efficiency and stability of our method to solve hybrid optimal control problems.?We propose an online monitoring framework of hybrid systems based on the above derivative-free optimization algorithm to improve the efficiency of real-time running hybrid systems.The new online monitoring framework combines the online verification and online control synthesis technique.To further improve the efficiency of our proposed control synthesis algorithm so that it can be applied to the online control synthesis area,we present a multi-phase control method by splitting the original task into multiple sub-tasks.The experiments on the complex synthesis show that the multi-phase control can generate feasible but still piece-wise optimal solutions in a very short time.?We implement the above hybrid optimal control synthesis algorithm and give a tool CDH.Meanwhile,to fully evaluate our proposed hybrid optimal control synthesis framework and online monitoring framework,we design a simulated train control system.Through the development on the hardware,we implement a self-control system for the smart car and then model it as a hybrid system.Finally,we conduct the online verification and online control synthesis experiment in a testbed with multiple simulated trains.The result shows that the efficiency of the whole train system can be improved a lot,since the train can still run safely without any emergency braking,according to the parameters from the online control synthesis module when the verification result is not safe.