A multiobjective approach to robust predictive control barrier functions for discrete-time systems

This paper introduces robust control barrier functions for uncertain parameter-varying control affine systems, where the parametric uncertainties can be time-varying and nonlinearly affecting the system dynamics and/or safety sets. In particular, we propose two methods based on mixed-monotone decomposition and concave bounding, where the controlled invariance condition remains linear in the control inputs despite nonlinear uncertainties. Moreover, we design alternative robust control Lyapunov functions where the control inputs also appear linearly; thus, these robust control barrier and Lyapunov functions can be coupled to obtain a quadratic program that can be solved online. Additionally, we propose two set-membership parameter estimation methods using polyhedral intersections and interval observers to reduce the conservatism of the robust approaches. Our robust approaches are observed to have comparable performance with adaptive approaches and robust safety guarantees, even when the (robust) adaptive methods may not.

Robust Control Barrier Functions for Control Affine Systems with Time-Varying Parametric Uncertainties

Application of Robust Control Barrier Function with Stochastic Disturbance Model for Discrete Time Systems

A systematic and complete method to design robust predictive controllers for unconstrained linear systems is proposed. The synthesis procedure is based on rigorous theoretical foundations, without resorting to approximations or ad hoc design guidelines, yet it remains a viable tool for practical application. A significant feature is that the robust predictive controller retains the servo performance of a nominal predictive controller designed using conventional methods. In addition, the robust predictive controller can be designed to guarantee perfect steady‐state rejection of asymptotically constant disturbances. The robust design method is developed for systems affected by unmodeled dynamics and is based on solving a discrete‐time model‐matching problem. It is shown that the robust controller can be classified legitimately as a predictive controller because it minimizes the same performance functional as the nominal predictive controller. An illustrative design example is given.

Safety is a critical feature of controller design for physical systems. When designing control policies, several approaches to guarantee this aspect of autonomy have been proposed, such as robust controllers or control barrier functions. However, these solutions strongly rely on the model of the system being available to the designer. As a parallel development, reinforcement learning provides model-agnostic control solutions but in general, it lacks the theoretical guarantees required for safety. Recent advances show that under mild conditions, control policies can be learned via reinforcement learning, which can be guaranteed to be safe by imposing these requirements as constraints of an optimization problem. However, to transfer from learning safety to learning safely, there are two hurdles that need to be overcome: (i) it has to be possible to learn the policy without having to re-initialize the system; and (ii) the rollouts of the system need to be in themselves safe. In this paper, we tackle the first issue, proposing an algorithm capable of operating in the continuing task setting without the need of restarts. We evaluate our approach in a numerical example, which shows the capabilities of the proposed approach in learning safe policies via safe exploration.

Learning Robust Hybrid Control Barrier Functions for Uncertain Systems

This paper proposes a synthetic robust model predictive control method with input mapping for the image-based visual servoing problem with constraints, where the novel control law is constructed by the robust control law designed offline and the online linear compensation of the past data. This proposed method can overcome the conservatism of robust model predictive control and reduce the online computational burden. The input mapping method is suitable for the image-based visual servoing system with no requirement of the slow time-varying model or time-invariant model as most adaptive control methods need. Its linear combination coefficients can be online optimized by solving a quadratic programming problem. The stability of the visual servoing system under our proposed method is proven, and its convergence speed is demonstrated to be faster than the traditional robust model predictive control. A real-time experiment on a six-degree-of-freedom manipulator with eye-in-hand construction is designed to evaluate the proposed method. The results indicate that besides the ability to handle the constraint and the singularity problem, our proposed method provides a faster convergence rate than several classic robust control methods, and improves the computational efficiency by an order of magnitude compared with the online robust predictive control method.

Control barrier functions have been demonstrated to be a useful method of ensuring constraint satisfaction for a wide class of controllers. However, the existing results are mostly restricted to continuous-time systems. Mechanical systems, including robots, are typically second-order systems in which the control occurs at the force/torque level. These systems have actuator, velocity, and position constraints (i.e., relative degree two) that are vital for safety and/or task execution. Additionally, mechanical systems are typically controlled digitally as sampled-data systems. The contribution of this article is twofold. The first contribution is the development of novel, robust control barrier functions that ensure constraint satisfaction for sampled-data systems in the presence of model uncertainty and allows for satisfaction of actuator constraints. The second contribution is the application of the proposed method to the challenging problem of robotic grasping in which a robotic hand must ensure that an object remains inside the grasp while manipulating it to the desired reference trajectory. A grasp constraint satisfying controller is proposed that can admit the existing nominal manipulation controllers from the literature while simultaneously ensuring no slip, no overextension (e.g., singular configurations), and no rolling off of the fingertips. Simulation and experimental results validate the proposed control for the robotic hand application.

The paper deals with the problem of robust predictive fault-tolerant control for non-linear discrete-time systems described by the Takagi-Sugeno models as well as application to the so-called Twin-Rotor system. Approach proposed in this paper is in fact series of three, i.e. it starts from fault estimation, which is subsequently compensated with a robust controller. While robust controller is designed without taking into account the input constraints, compensation feasibility is proven by introducing invariant set of states, which takes into account the input constraints. If the current state do not belong to a robust invariant set, appropriate predictive control actions are performed. This appealing phenomenon makes it possible to enlarge the domain of attraction, making the proposed approach an efficient solution for the fault-tolerant control. The final part of the paper shows an illustrative example of proposed approach to the Twin-Rotor system.

This paper studies control synthesis for a general class of nonlinear, control-affine dynamical systems under additive disturbances and state-estimation errors. We enforce forward invariance of static and dynamic safe sets and convergence to a given goal set within a user-defined time in the presence of input constraints. We use robust variants of control barrier functions (CBF) and fixed-time control Lyapunov functions (FxT-CLF) to incorporate a class of additive disturbances in the system dynamics, and state-estimation errors. To solve the underlying constrained control problem, we formulate a quadratic program and use the proposed robust CBF-FxT-CLF conditions to compute the control input. We showcase the efficacy of the proposed method on a numerical case study involving multiple underactuated marine vehicles.

This paper addresses the problem of safety-critical control for stochastic control systems. Constrained optimal control problems can be sub-optimally reduced to a sequence of quadratic programs by using Control Barrier Functions (CBFs). The recently proposed High Order CBFs (HOCBFs) can accommodate constraints of arbitrary relative degree. The main challenge of this HOCBF method for stochastic systems lies in the fact that intractable high-order derivatives of random variables will be involved. Meanwhile, the system tends to be very conservative such that the system state tends to stay far away from safe set boundary, which significantly limits the system performance. To avoid high-order derivatives of random variables, we propose a recursively robust HOCBF (rrHOCBF) that iteratively replace random variables by their bounds in the derivation of the HOCBF constraint. We further propose a non-conservative and robust HOCBF (nrHOCBF) to address the conservativeness issue in this robust control method by introducing adaptive terms to the bounds of random variables. We provably show the safety guarantees of the proposed rrHOCBFs and nrHOCBFs. A case study of 2D obstacle avoidance is presented to demonstrate the effectiveness and advantages of the proposed method when compared to existing approaches.

This paper presents a robust model-based predictive control (MPC) strategy for temperature control of an air-conditioning system, which consists of multiple local-loop processes and each process suffers from different dynamics uncertainties or variations. When an appropriate sampling period is chosen to discretise the system for computer control, a state-space discrete model with an uncertainty polytope is developed to describe the mixing uncertainties of these type of systems. The main benefit of the proposed description is that robust model predictive control can be easily used to design a robust controller for such a system while taking account of constraints associated with this system. A linear matrix inequality-based MPC algorithm is employed for control design. Case study was conducted on a dynamic simulation platform of an air-conditioning system, which evaluated the developed strategy in various simulation tests by comparing with the conventional PID control. Results demonstrated that the developed strategy is able to deal with constraints and allows stable and robust control while maintaining acceptable thermal comfort. Although the strategy is illustrated and validated using a constant air volume air-conditioning system, it can be applied to other constraint HVAC processes suffering from similar uncertainties. Practical applications: The main benefit of the developed strategy (including the proposed description and the adopted robust control algorithm) for practical application is that uncertainties and constraints can be dealt with simultaneously in one framework. Constraints in HVAC systems exist due to the application of actuators, for example, the rate limit considered in the paper. Taking account of constraints is useful to prevent unnecessary damages to equipments and maintain the system operating in a safe mode. Most importantly, the control objectives can be achieved in a constraint manner. The consideration of uncertainties, probably due to the changes of operating environment, is useful to release the work of accurate modelling of HVAC processes and online tuning of controllers.

This paper presents a method for guaranteeing the safety of a system with time‐varying parameters. First, we extend Dynamic Regressor Extension and Mixing to estimate time‐varying parameters with a finite‐time update rule, and present a bound on the estimation error. In the case of a constant parameter, we provide an improved lower bound on the update gain compared with the literature. Lastly, the parameter error bound is used to provide a Robust adaptive Control Barrier Function for systems with time‐varying parameters. We conduct a numerical simulation of a system with time‐varying parameters. The presented estimation method estimates the parameters with a smaller mean‐square error compared with methods from the literature. The presented control barrier function can keep the system safe despite parametric uncertainties.

This thesis presents a robust predictive control applied to the converter connected to the electrical grid. In this case, the converter is connected to a renewable energy source, which can be wind, solar, hydro, among others. The mains converter is driven by the robust predictive control modulated through the converter model controlling the injected currents. The controller is designed based on a dynamic mathematical model of the grid. The mathematical model and the control design are simulated using the tool SimPowerSystems -Matlab / Simulink. The experimental results are obtained on a test bench using Digital Signal Process which calculates the voltage applied to the converter based on the control law from the model. And also a robust portion is calculated to compensate for possible uncertainties in the system (plant plus controller). To validate the implemented control proposal, which uses the principles of predictive and robust control, experimental tests in different modes of operation are presented. Finally, a comparison was made with two conventional predictive control techniques to prove the effectiveness of the controller proposed in this thesis.

This paper develops a novel homography-based visual servo control method for the vertical take-off and landing (VTOL) unmanned aerial vehicle (UAV) tracking the trajectory of a 6 degrees of freedom (6-DOF) moving ship. Different from the classical homography-based visual servoing which is only suitable for the trajectory tracking of a planar moving target, an extended homography-based visual servoing framework is proposed to track the trajectory of a 6-DOF moving target regardless of its time-varying rotational motion. Taking entries in the homography matrix as feedback, the visual dynamics of UAV is established and decoupled into a translational motion sub-dynamics and an attitude sub-dynamics based on the hierarchical control strategy. In the translational motion subsystem, the robust controller is designed by embedding the nonlinear differentiator, the adaptive method, and a smooth saturation model in the backstepping control scheme. The saturation model is introduced to generate the constrained control inputs to ensure the nonsingular attitude extraction and help the visual points remain in the camera's field of view (FoV) simultaneously. In the attitude subsystem, a robust state-constrained control method is proposed by utilizing a robust control barrier function (RCBF), the quadratic programming (QP) and a saturation model to guarantee the visibility, where RCBF can accommodate unknown dynamics. The theoretical analysis demonstrates the asymptotic stability of the closed-loop system. Simulations are carried out to further validate the controller performance.