Safety-critical Constraints Research Articles

Ultra-Fast Nonlinear Model Predictive Control for Motion Control of Autonomous Light Motor Vehicles

Advanced Driver Assistance System (ADAS) is the latest buzzword in the automotive industry aimed at reducing human errors and enhancing safety. In ADAS systems, the choice of control strategy is not straightforward due to the highly complex nonlinear dynamics, control objectives, and safety critical constraints. Nonlinear Model Predictive Control (NMPC) has evolved as a favorite option for optimal control due to its ability to handle such constrained, Multi-Input Multi-Output (MIMO) systems efficiently. However, NMPC suffers from a bottleneck of high computational complexity, making it unsuitable for fast real-time applications. This paper presents a generic framework using Successive Online Linearization-based NMPC (SOL-NMPC) for for the control in ADAS. The nonlinear system is linearized and solved using Linear Model Predictive Control every iteration. Furthermore, offset-free MPC is developed with the Extended Kalman Filter for reducing model mismatch. The developed SOL-NMPC is validated using the 14-Degrees-of-Freedom (DoF) model of a D-class light motor vehicle. The performance is simulated in matlab/Simulink and validated using the CarSim® software (Version 2016). The real-time implementation of the proposed strategy is tested in the Hardware-In-the-Loop (HIL) co-simulation using the STM32-Nucleo-144 development board. The detailed performance analysis is presented along with time profiling. It can be seen that the loss of accuracy can be counteracted by the fast response of the proposed framework.

Formal modelling and verification of autonomous reasoning based flight simulation system

The emerging trends towards intelligent computing have drastically changed the human lifestyle in every facet of their lives. Due to the swift escalation of smart systems and emerging technologies, human life has become much more dependent and even more addicted to fulfilling their desire using smart and tiny resource-bounded gadgets. This revolution has evolved towards autonomous decision support systems. Autonomous decision support systems have the ability to acquire information autonomously, reason the information, and adapt behavior accordingly. As these systems are deployed in a highly decentralized environment and exhibit complex adaptive behavior, however, the inconsistent nature of information may raise different challenging issues. This paper presents a multi-agent environmentally-aware framework for modeling and reasoning flight management systems. This system has a sound reasoning mechanism to execute and monitor flight control activities while considering liveness and safety-critical constraints. We use the UPPAAL model checker to formally analyze the system’s behavior and verify correctness properties.

Safety-Critical Stabilizing Design of Switched Linear Autonomous Systems

For continuous-time switched linear autonomous systems, this work addresses the stabilization problem under safety-critical constraints. Given an origin-symmetric region that any state trajectory should be stayed, we seek to design a switching law to achieve both stability and safety. The main approach is to characterize, both theoretically and algorithmically, the safe initial set that any initial state within the set could stay in the given safety region with a properly designed switching law. Technically, we develop a design procedure that could approximate the safe initial set with the help of the pathwise state feedback switching strategy. A third-order example is presented to validate the effectiveness of the proposed methodology.

Safety-Critical and Flexible Cooperative On-Ramp Merging Control of Connected and Automated Vehicles in Mixed Traffic

Cooperative on-ramp merging control for connected and automated vehicles (CAVs) can effectively improve traffic throughput and vehicle fuel efficiency at highway on-ramp merging bottlenecks. However, in the mixed traffic scenario where CAVs and human-driven vehicles (HDVs) coexist, the uncertain maneuvers of human drivers pose a major challenge to merging control in terms of safety and flexibility. To this end, this paper proposes a hierarchical cooperative on-ramp merging control strategy for CAVs to optimize flexible trajectories with safety guarantees in mixed traffic. First, the on-ramp merging control problem for CAVs is considered in the case of a three-vehicle coordination, resulting in an optimal control problem (OCP) coordinating on-ramp and main-lane CAVs for efficient operation while satisfying multiple safety-critical constraints. Second, a two-level hierarchical control architecture is developed to solve the OCP with mixed state-control constraints. The upper-level planner solves an unconstrained OCP with Pontryagin’s Minimum Principle to calculate an expected merging position, which is embedded in the variable time headway of safe merging constraints in the lower-level controller. Then, the controller converts the nonlinear OCP with safety-critical constraints to a quadratic programing (QP) problem by exploiting Control Barrier Functions (CBFs) and Control Lyapunov Functions (CLFs). By solving the QP efficiently, the time and energy efficient trajectory for each CAV is obtained. In addition, a receding horizon control framework is employed, which enables CAVs to determine flexible merging opportunity and tackle the disturbances caused by HDVs. Finally, comprehensive simulation results show that the proposed cooperative on-ramp merging strategy has potential in enabling merging flexibility, improving traffic efficiency and energy economy in real time.

Robust peak-to-peak gain analysis using integral quadratic constraints

This work provides a framework to compute an upper bound on the robust peak-to-peak gain of discrete-time uncertain linear systems using integral quadratic constraints (IQCs). Such bounds are of particular interest in the computation of reachable sets and the l1-norm, as well as when safety-critical constraints need to be satisfied pointwise in time. The use of p-hard IQCs with a terminal cost enables us to deal with a wide variety of uncertainty classes, for example, we provide p-hard IQCs with a terminal cost for the class of parametric uncertainties. This approach unifies, generalizes, and significantly improves state-of-the-art methods, which is also demonstrated in a numerical example.

On Tuning Parameterized Control Policies Online for Safety-Critical Systems -Applied to Biomedical Systems

There are different approaches to tune a control policy that would result in a desired closed-loop performance. The typical design flow involves tuning the control policies offline using (high-fidelity) simulators until satisfactory performance is achieved. This paper on the other hand, considers the problem of tuning parameterized control policies directly by interacting with the real system that also has safety-critical constraints. We use safe Bayesian optimization using interior-point methods to tune the parameterized control policy online that guarantees constraint satisfaction with high probability. The proposed framework is applied to a personalized artificial pancreas system for type 1 diabetes. The paper shows that the parameterized control policy used for blood glucose regulation can be safely tuned to personalize the controller for each individual patient using our approach and thus improve its performance.

Reinforcement Learning Enabled Safety-Critical Tracking of Automated Vehicles with Uncertainties via Integrated Control-Dependent, Time-Varying Barrier Function, and Control Lyapunov Function

Model uncertainties are considered in a learning-based control framework that combines control dependent barrier function (CDBF), time-varying control barrier function (TCBF), and control Lyapunov function (CLF). Tracking control is achieved by CLF, while safety-critical constraints during tracking are guaranteed by CDBF and TCBF. A reinforcement learning (RL) method is applied to jointly learn model uncertainties that related to CDBF, TCBF, and CLF. The learning-based framework eventually formulates a quadratic programming (QP) with different constraints of CDBF, TCBF and CLF involving model uncertainties. It is the first time to apply the proposed learning-based framework for safety-guaranteed tracking control of automated vehicles with uncertainties. The control performances are validated for two different single-lane change maneuvers via Simulink/CarSim® co-simulation and compared for the cases with and without learning. Moreover, the learning effects are discussed through explainable constraints in the QP formulation.

Exponential Control Lyapunov-Barrier Function Using a Filtering-Based Concurrent Learning Adaptive Approach

The state-of-the-art quadratic-program-based control Lyapunov-barrier function (QP-CLBF) is a powerful control approach to balance safety and stability in an optimal fashion. However, under this approach, modeling inaccuracies may degrade the performance of closed-loop systems and cause violation or restriction of safety-critical constraints. This article presents an adaptive QP-CLBF approach for a class of nonlinear systems in the presence of parameter uncertainties with an unknown control coefficient. We begin by presenting a filtering-based concurrent learning (FCL) adaptive technique to guarantee simultaneous exponential convergence of system parameters and control coefficient. The proposed FCL extends and encompasses the baseline concurrent learning technique, which was developed to achieve exponential convergence of either system parameters exclusively or control coefficient while relying on the estimation of state derivatives using numerical smoothing. The proposed FCL adaptive method is then unified with a modified version of QP-CLBF to achieve exponential convergence of system parameters, control coefficient, and control Lyapunov and control barrier functions while establishing safety with the largest safe region. Under this unification, all results are exponential in the presence of modeling error without the need for numerical methods to estimate state derivatives. This is formally proven by employing a Lyapunov argument. Simulations are finally carried out to validate the theoretical results.

Tuning particle accelerators with safety constraints using Bayesian optimization

Tuning machine parameters of particle accelerators is a repetitive and time-consuming task that is challenging to automate. While many off-the-shelf optimization algorithms are available, in practice their use is limited because most methods do not account for safety-critical constraints in each iteration, such as loss signals or step-size limitations. One notable exception is safe Bayesian optimization, which is a data-driven tuning approach for global optimization with noisy feedback. We propose and evaluate a step-size limited variant of safe Bayesian optimization on two research facilities of the PSI: (a) the SwissFEL and (b) HIPA. We report promising experimental results on both machines, tuning up to 16 parameters subject to 224 constraints.

Chance constrained policy optimization for process control and optimization

Chemical process optimization and control are affected by (1) plant-model mismatch, (2) process disturbances, and (3) constraints for safe operation. Reinforcement learning by policy optimization would be a natural way to solve this due to its ability to address stochasticity, plant-model mismatch, and directly account for the effect of future uncertainty and its feedback in a proper closed-loop manner; all without the need of an inner optimization loop. One of the main reasons why reinforcement learning has not been considered for industrial processes (or almost any engineering application) is that it lacks a framework to deal with safety critical constraints. Present algorithms for policy optimization use difficult-to-tune penalty parameters, fail to reliably satisfy state constraints or present guarantees only in expectation. We propose a chance constrained policy optimization (CCPO) algorithm which guarantees the satisfaction of joint chance constraints with a high probability — which is crucial for safety critical tasks. This is achieved by the introduction of constraint tightening (backoffs), which are computed simultaneously with the feedback policy. Backoffs are adjusted with Bayesian optimization using the empirical cumulative distribution function of the probabilistic constraints, and are therefore self-tuned. This results in a general methodology that can be imbued into present policy optimization algorithms to enable them to satisfy joint chance constraints with high probability. We present case studies that analyse the performance of the proposed approach.

Safe Bayesian Optimization Using Interior-Point Methods—Applied to Personalized Insulin Dose Guidance

This paper considers the problem of Bayesian optimization for systems with safety-critical constraints, where both the objective function and the constraints are unknown, but can be observed by querying the system. In safety-critical applications, querying the system at an infeasible point can have catastrophic consequences. Such systems require a safe learning framework, such that the performance objective can be optimized while satisfying the safety-critical constraints with high probability. In this paper we propose a safe Bayesian optimization framework that ensures that the points queried are always in the interior of the partially revealed safe region, thereby guaranteeing constraint satisfaction with high probability. The proposed interior-point Bayesian optimization framework can be used with any acquisition function, making it broadly applicable. The performance of the proposed method is demonstrated using a personalized insulin dosing application for patients with type 1 diabetes.

Robust Safety-Critical Control for Dynamic Robotics

We present a novel method of optimal robust control through quadratic programs that offers tracking stability while subject to input and state-based constraints as well as safety-critical constraints for nonlinear dynamical robotic systems in the presence of model uncertainty. The proposed method formulates robust control Lyapunov and barrier functions to provide guarantees of stability and safety in the presence of model uncertainty. We evaluate our proposed control design on dynamic walking of a five-link planar bipedal robot subject to contact force constraints as well as safety-critical precise foot placements on stepping stones, all while subject to model uncertainty. We conduct preliminary experimental validation of the proposed controller on a rectilinear spring-cart system under different types of model uncertainty and perturbations.

Safety-centered process control design based on dynamic safe set

The objective of this research is to develop an approach for the process control design problem with safety as the primary target. The work proposes the concept of dynamic safe set (DSS) to characterize and evaluate the safeness of a closed-loop system.The DSS is defined as a set of initial states of the process that guarantees safe operation, which is represented by a set of safety-critical constraints that is to be satisfied at all times. The DSS calculation accounts for potential safety threatening disturbances that may significantly affect the dynamics of the system. An addon control scheme based on the DSS concept is proposed to guide the system when it is under sudden and large set point changes that may be needed during abnormal situations. Existing system theoretic concepts of maximal output admissible sets is used to mathematically formulate and determine the DSS. The concept of dynamic safety margin (DSM) is proposed as a quantitative measure of the size of DSS. An approach based on the DSS and DSM concepts for process control design with the objective to maximize safety, subject to other performance constraints, is proposed.The approach is tested on an exothermic CSTR case study. The results showed the strong effect of steady state operating conditions, control parameters and actuator design parameters on DSM. A grid of design parameters that includes the reactor set point, the controller parameters, and the heat exchanger design parameter was analyzed. The analysis led to identifying a maximally safe control system design. The proposed approach allowed to formulate the process control design problem by bringing safety upfront, without compromising performance metrics.

Admissible sets for slowly-varying discrete-time systems

This note describes a method to calculate admissible sets for dynamical systems with slowly-varying parameters. A set of initial states is said to be admissible if all state trajectories starting within this set respect safety-critical constraints for all future time instances. For many classes of systems, the Maximal Admissible Set (MAS) equals the Maximal Robust Positive Invariant (MRPI) set. Therefore, much of the literature focus on algorithms that produce (approximations of) the MRPI set. However, for slowly-varying systems it turns out that the MAS can be larger than the MRPI set. A property referred to as the M-proximal contraction property is defined for such systems to state sufficient conditions for sets to be admissible. It is then shown that Algorithm 2 produces an admissible set that is a superset of the MRPI set.

Data-Based Nonlinear Model Identification in Economic Model Predictive Control

Abstract Many chemical/petrochemical processes in industry are not completely modeled from a first-principles perspective because of the complexity of the underlying physico-chemical phenomena and the cost of obtaining more accurate, physically relevant models. System identification methods have been utilized successfully for developing empirical, though not necessarily physical, models for advanced model-based control designs such as model predictive control (MPC) for decades. However, a fairly recent development in MPC is economic model predictive control (EMPC), which is an MPC formulated with an economics-based objective function that may operate a process in a dynamic (i.e., off steady-state) fashion, in which case the details of the process model become important for obtaining sufficiently accurate state predictions away from the steady-state, and the physics and chemistry of the process become important for developing meaningful profit-based objective functions and safety-critical constraints. Therefore, methods must be developed for obtaining physically relevant models from data for EMPC design. While the literature regarding developing models from data has rapidly expanded in recent years, many new techniques require a model structure to be assumed a priori, to which the data is then fit. However, from the perspective of developing a physically meaningful model for a chemical process, it is often not obvious what structure to assume for the model, especially considering the often complex nonlinearities characteristic of chemical processes (e.g., in reaction rate laws). In this work, we suggest that the controller itself may facilitate the identification of physically relevant models online from process operating data by forcing the process state to nonroutine operating conditions for short periods of time to obtain data that can aid in selecting model structures believed to have physical significance for the process and, subsequently, identifying their parameters. Specifically, we develop EMPC designs for which the objective function and constraints can be changed for short periods of time to obtain data to aid in model structure selection. For one of the developed designs, we incorporate Lyapunov-based stability constraints that allow closed-loop stability and recursive feasibility to be proven even as the online “experiments” are performed. This new design is applied to a chemical process example to demonstrate its potential to facilitate physics-based model identification without loss of closed-loop stability. This work therefore reverses a question that has been of interest to the control community (i.e., how new techniques for developing models from data can be useful for control of chemical processes) to ask how control may be utilized to impact the use of these techniques for the identification of physically relevant process dynamic models that can aid in improving process operation and control for economic and safety purposes.