Correct-By-Construction Control Synthesis for Systems with Disturbance and Uncertainty

This dissertation focuses on correct-by-construction control synthesis for Cyber-Physical Systems (CPS) under model uncertainty and disturbance. CPSs are systems that interact with the physical world and perform complicated dynamic tasks where safety is often the overriding factor. Correct-by-construction control synthesis is a concept that provides formal performance guarantees to closed-loop systems by rigorous mathematic reasoning. Since CPSs interact with the environment, disturbance and modeling uncertainty are critical to the success of the control synthesis. Disturbance and uncertainty may come from a variety of sources, such as exogenous disturbance, the disturbance caused by co-existing controllers and modeling uncertainty. To better accommodate the different types of disturbance and uncertainty, the verification and control synthesis methods must be chosen accordingly. Four approaches are included in this dissertation. First, to deal with exogenous disturbance, a polar algorithm is developed to compute an avoidable set for obstacle avoidance. Second, a supervised learning based method is proposed to design a good student controller that has safety built-in and rarely triggers the intervention of the supervisory controller, thus targeting the design of the student controller. Third, to deal with the disturbance caused by co-existing controllers, a Lyapunov verification method is proposed to formally verify the safety of coexisting controllers while respecting the confidentiality requirement. Finally, a data-driven approach is proposed to deal with model uncertainty. A minimal robust control invariant set is computed for an uncertain dynamic system without a given model by first identifying the set of admissible models and then simultaneously computing the invariant set while selecting the optimal model. The proposed methods are applicable to many real-world applications and reflect the notion of using the structure of the system to achieve performance guarantees without being overly conservative.PHDMechanical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/145933/1/chenyx_1.pd

Invariant Set Estimation for Piecewise Affine Dynamical Systems Using Piecewise Affine Barrier Function

This paper introduces an algorithm for approximating the invariant set of closed-loop controlled dynamical systems identified using ReLU neural networks or piecewise affine PWA functions, particularly addressing the challenge of providing safety guarantees for ReLU networks commonly used in safety-critical applications. The invariant set of PWA dynamical system is estimated using ReLU networks or its equivalent PWA function. This method entails formulating the barrier function as a PWA function and converting the search process into a linear optimization problem using vertices. We incorporate a domain refinement strategy to increase flexibility in case the optimization does not find a valid barrier function. Moreover, the objective of optimization is to maximize the invariant set based on the current partition. Our experimental results demonstrate the effectiveness and efficiency of our approach, demonstrating its potential for ensuring the safety of PWA dynamical systems.Comment: Preprint submitted to European Journal of Control, 9 pages, 7 figure

A recurrent neural network applied to optimal motion control of mobile robots with physical constraints

Conventional solutions, such as the conventional recurrent neural network (CRNN) and gradient recurrent neural network (GRNN), for the motion control of mobile robots in the unified framework of recurrent neural network (RNN) are difficult to simultaneously consider both criteria optimization and physical constraints. The limitation of the RNN solution may lead to the damage of mobile robots for exceeding physical constraints during the task execution. To overcome this limitation, this paper proposes a novel inequality and equality constrained optimization RNN (IECORNN) to handle the motion control of mobile robots. Firstly, the real-time motion control problem with both criteria optimization and physical constraints is skillfully converted to a real-time equality system by leveraging the Lagrange multiplier rule. Then, the detailed design process for the proposed IECORNN is presented together with the neural network architecture developed. Afterward, theoretical analyses on the motion control problem conversion equivalence, global stability, and exponential convergence property are rigorously provided. Finally, two numerical simulation verifications and extensive comparisons with other existing RNNs, e.g., the CRNN and the GRNN, based on the mobile robot for two different path-tracking applications sufficiently demonstrate the effectiveness and superiority of the proposed IECORNN for the real-time motion control of mobile robots with both criteria optimization and physical constraints. This work makes progresses in both theory as well as practice, and fills the vacancy in the unified framework of RNN in motion control of mobile robots

Control and safety of fully actuated and underactuated nonlinear systems: from adaptation to robustness to optimality

The state-of-the-art quadratic program-based control Lyapunov-control barrier function (QP-CLBF) is a powerful control approach to balance safety and stability in a pointwise optimal fashion. However, under this approach, modeling inaccuracies may degrade the performance of closed-loop systems and cause a violation of safety-critical constraints. This thesis extends the recently-developed QP-CLBF through the derivation of five novel robust quadratic program-based adaptive control approaches for fully actuated and underactuated nonlinear systems with a view toward adapting to unknown parameters, being robust to unmodeled dynamics and disturbances, ensuring the system remains in safe sets and being optimal with respect in a pointwise fashion. Simulation and quantitative results demonstrate the superiority of proposed approaches over the baseline methods.Ph.D

Reactive Gait Composition with Stability: Dynamic Walking amidst Static and Moving Obstacles

This paper presents a modular approach to motion planning with provable stability guarantees for robots that move through changing environments via periodic locomotion behaviors. We focus on dynamic walkers as a paradigm for such systems, although the tools developed in this paper can be used to support general compositional approaches to robot motion planning with Dynamic Movement Primitives (DMPs). Our approach ensures a priori that the suggested plan can be stably executed. This is achieved by formulating the planning process as a Switching System with Multiple Equilibria (SSME) and proving that the system's evolution remains within explicitly characterized trapping regions in the state space under suitable constraints on the frequency of switching among the DMPs. These conditions effectively encapsulate the low-level stability limitations in a form that can be easily communicated to the planner to guarantee that the suggested plan is compatible with the robot's dynamics. Furthermore, we show how the available primitives can be safely composed online in a receding horizon manner to enable the robot to react to moving obstacles. The proposed framework is applied on 3D bipedal walking models under common modeling assumptions, and offers a modular approach towards stably integrating readily available low-level locomotion control and high-level planning methods.Comment: 18 pages, 10 figure

Sliding Mode Control

The main objective of this monograph is to present a broad range of well worked out, recent application studies as well as theoretical contributions in the field of sliding mode control system analysis and design. The contributions presented here include new theoretical developments as well as successful applications of variable structure controllers primarily in the field of power electronics, electric drives and motion steering systems. They enrich the current state of the art, and motivate and encourage new ideas and solutions in the sliding mode control area

Inductive Certificate Synthesis for Control Design

The focus of this thesis is developing a framework for designing correct-by-construction controllers using control certificates. We use nonlinear dynamical systems to model the physical environment (plants). The goal is to synthesize controllers for these plants while guaranteeing formal correctness w.r.t. given specifications. We consider different fundamental specifications including stability, safety, and reach-while-stay. Stability specification states that the execution traces of the system remain close to an equilibrium state and approach it asymptotically. Safety specification requires the execution traces to stay in a safe region. Finally, for reach-while-stay specification, safety is needed until a target set is reached.The design task consists of two phases. In the first phase, the control design problem is reduced to the question of finding a control certificate. More precisely, the goal of the first phase is to define a class of control certificates with a specific structure. This definition should guarantee the following: ``Having a control certificate, one can systematically design a controller and prove its correctness at the same time."The goal in the second phase is to find such a control certificate. We define a potential control certificate space (hypothesis space) using parameterized functions. Next, we provide an inductive search framework to find proper parameters, which yield a control certificate. Finally, we evaluate our framework. We show that discovering control certificates is practically feasible and demonstrate the effectiveness of the automatically designed controllers through simulations and real physical systems experiments

Applicable Solutions in Non-Linear Dynamical Systems

From Preface: The 15th International Conference „Dynamical Systems - Theory and Applications” (DSTA 2019, 2-5 December, 2019, Lodz, Poland) gathered a numerous group of outstanding scientists and engineers who deal with widely understood problems of theoretical and applied dynamics. Organization of the conference would not have been possible without great effort of the staff of the Department of Automation, Biomechanics and Mechatronics of the Lodz University of Technology. The patronage over the conference has been taken by the Committee of Mechanics of the Polish Academy of Sciences and Ministry of Science and Higher Education of Poland. It is a great pleasure that our event was attended by over 180 researchers from 35 countries all over the world, who decided to share the results of their research and experience in different fields related to dynamical systems. This year, the DSTA Conference Proceedings were split into two volumes entitled „Theoretical Approaches in Non-Linear Dynamical Systems” and „Applicable Solutions in Non-Linear Dynamical Systems”. In addition, DSTA 2019 resulted in three volumes of Springer Proceedings in Mathematics and Statistics entitled „Control and Stability of Dynamical Systems”, „Mathematical and Numerical Approaches in Dynamical Systems” and „Dynamical Systems in Mechatronics and Life Sciences”. Also, many outstanding papers will be recommended to special issues of renowned scientific journals.Cover design: Kaźmierczak, MarekTechnical editor: Kaźmierczak, Mare