In this paper we propose a constrained guaranteed cost robust model predictive controller (GCMPC) for uncertain discrete time systems. This controller was developed based on a quadratic cost functional and guarantee robustness with respect to quadratically bound uncertainties. Such a class of problems is currently intractable by Min-Max Robust Model Predictive Controllers without polytopic approximations of the uncertainties. The proposed technique is computationally more efficient then an enumeration-based approach and requires only a Quadratically Constrained Quadratic Problem (QCQP) optimization, whereas LMI-based GCMPC approaches require a Semi-Definite Programming (SDP) optimization.
A new formulation of Stochastic Model Predictive Output Feedback Control is presented and analyzed as a translation of Stochastic Optimal Output Feedback Control into a receding horizon setting. This requires lifting the design into a framework involving propagation of the conditional state density, the information state, via the Bayesian Filter and solution of the Stochastic Dynamic Programming Equation for an optimal feedback policy, both stages of which are computationally challenging in the general, nonlinear setup. The upside is that the clearance of three bottleneck aspects of Model Pred…
Road traffic crashes have been the leading cause of death among young people. Most of these accidents occur when the driver becomes distracted and a loss-of-control situation occurs. Steer-by-Wire systems were recently proposed as an alternative to mitigate such accidents. This technology enables the decoupling of the front wheel steering angles from the driver hand wheel angle and, consequently, the measurement of road/tire friction limits and the development of novel control systems capable of ensuring vehicle stabilization and safety. However, vehicle safety boundaries are highly dependent …
We propose a tube-based guaranteed cost model predictive controller considering a homothetic formulation for constrained linear systems subject to multiplicative structured norm-bounded uncertainties. It provides an upper bound to the general min-max model predictive control. The invariance property of the proposed tube holds for any arbitrary scaling. It yields a second-order cone programming problem which is less computationally expensive than standard semi-definite programming problems. We also present a numerical example with a comparative study among the proposed approach, an open-loop gu…
In this paper, we propose state- and static output-feedback generalized guaranteed cost control (GCC) approaches for discrete-time linear systems subject to norm-bounded structured parametric uncertainties. This method enables the convex synthesis for a more general class of systems, where uncertainties are uncorrelated block diagonal, and no feed-through uncertainty is multiplicative with control input ones. It also provides necessary and sufficient conditions for state-feedback and sufficient conditions for static output-feedback. We also present a comparative study among the proposed contro…
Control and estimation on large-scale social networks often necessitate the availability of models for the interactions amongst the agents. However characterizing accurate models of social interactions pose new challenges due to inherent complexity and unpredictability. Moreover, model uncertainty becomes more pronounced for large-scale networks. For certain classes of social networks, the layering structure allows a compositional approach. In this paper, we present such an approach to determine performance guarantees on layered networks with inherent model uncertainties. A factorization metho…
Networked Control Systems (NCSs) often suffer from random packet dropouts which deteriorate overall system's stability and performance. To handle the ill effects of random packet losses in feedback control systems, closed over communication network, a state feedback controller with predictive gains has been designed. To achieve improved performance, an optimization based controller design framework has been proposed in this paper with Linear Matrix Inequality (LMI) constraints, to ensure guaranteed stability. Different conflicting objective functions have been optimized with Non-dominated Sort…
We present a data-driven model predictive control scheme for chance-constrained Markovian switching systems with unknown switching probabilities. Using samples of the underlying Markov chain, ambiguity sets of transition probabilities are estimated which include the true conditional probability distributions with high probability. These sets are updated online and used to formulate a time-varying, risk-averse optimal control problem. We prove recursive feasibility of the resulting MPC scheme and show that the original chance constraints remain satisfied at every time step. Furthermore, we show…
The development of control techniques to maintain vehicle stability under possible loss-of-control scenarios is essential to the safe deployment of autonomous ground vehicles in public scenarios. In this paper, we propose a tube-based guaranteed cost model predictive controller for autonomous vehicles able to avoid front and rear tire saturation and to track a provided reference trajectory up to the limits of handling of the vehicle. Such an approach ensures the vehicle will remain within its safe operational envelope; therefore, guaranteeing both stability and performance of the vehicle, incl…
We propose a robust adaptive Model Predictive Control (MPC) strategy with online set-based estimation for constrained linear systems with unknown parameters and bounded disturbances. A sample-based test applied to predicted trajectories is used to ensure convergence of parameter estimates by enforcing a persistence of excitation condition on the closed loop system. The control law robustly satisfies constraints and has guarantees of feasibility and input-to-state stability. Convergence of parameter set estimates to the actual system parameter vector is guaranteed under conditions on reachabili…
This paper presents a novel adaptive control methodology for uncertain systems with time-varying unknown parameters and time-varying bounded disturbance. The adaptive controller ensures uniformly bounded transient and asymptotic tracking for system's both signals, input and output, simultaneously. The performance bounds can be systematically improved by increasing the adaptation gain. Simulations of a robotic arm with time-varying friction verify the theoretical findings.
In this paper, we present Robust Model Predictive Control (MPC) problems with adjustable uncertainty sets. In contrast to standard Robust MPC problems with known uncertainty sets, we treat the uncertainty sets in our problems as additional decision variables. In particular, given a metric for adjusting the uncertainty sets, we address the question of determining the optimal size and shape of those uncertainty sets, while ensuring robust constraint satisfaction. The focus of this paper is on ensuring constraint satisfaction over an infinite horizon, also known as persistent feasibility. We show…
We are concerned with the design of Model Predictive Control (MPC) schemes such that asymptotic stability of the resulting closed loop is guaranteed even if the linearization at the desired set point fails to be stabilizable. Therefore, we propose to construct the stage cost based on the homogeneous approximation and rigorously show that applying MPC yields an asymp-totically stable closed-loop behavior if the homogeneous approximation is asymptotically null controllable. To this end, we verify cost controllability-a condition relating the current state, the stage cost, and the growth of the v…
This paper investigates adaptive model predictive control (MPC) for a class of constrained linear systems with unknown model parameters. This is also posed as the dual control problem consisting of system identification and regulation. We first propose an online strategy for simultaneous unknown parameter identification and uncertainty set estimation based on the recursive least square technique. The designed strategy provides a contractive sequence of uncertain parameter sets, and the convergence of parameter estimates is achieved under certain conditions. Second, by integrating tube MPC with…
In this paper we investigate feedback control techniques for the COVID-19 pandemic which are able to guarantee that the capacity of available intensive care unit beds is not exceeded. The control signal models the social distancing policies enacted by the local government. We propose a control design based on the bang-bang funnel controller which is robust with respect to uncertainties in the parameters of the epidemiological model and only requires measurements of the number of individuals who require medical attention. Therefore, it may serve as a first step towards a reliable decision makin…
This paper presents a computationally efficient robust model predictive control law for discrete linear time invariant systems subject to additive disturbances that may depend on the state and/or input norms. Despite the dependency being non-convex, we are able to capture it exactly for input dependency and approximately for state dependency in at most a second order cone programming problem. The formulation has linear complexity in the planning horizon length. The approach is thus amenable to efficient real-time implementation with a guarantee on recursive feasibility and global optimality. R…
A probabilistic performance-oriented controller design approach based on polynomial chaos expansion and optimization is proposed for flight dynamic systems. Unlike robust control techniques where uncertainties are conservatively handled, the proposed method aims at propagating uncertainties effectively and optimizing control parameters to satisfy the probabilistic requirements directly. To achieve this, the sensitivities of violation probabilities are evaluated by the expansion coefficients and the fourth moment method for reliability analysis, after which an optimization that minimizes failur…
Towards Guaranteed Optimal PID Tuning for Uncertain Nonlinear Systems
State Key Laboratory of Mathematical Sciences, AMSS, Chinese Academy of Sciences（中国科学院数学与系统科学研究院数学科学国家重点实验室）；School of Mathematical Sciences, University of Chinese Academy of Sciences（中国科学院大学数学科学学院）
This paper involves the innovative development of a symmetric Gauss-Seidel ADMM algorithm to solve the H-infinity guaranteed cost control problem. In the presence of parametric uncertainties, the H-infinity guaranteed cost control problem generally leads to the large-scale optimization. This is due to the exponential growth of the number of the extreme systems involved with respect to the number of parametric uncertainties. In this work, through a variant of the Youla-Kucera parameterization, the stabilizing controllers are parameterized in a convex set; yielding the outcome that the H-infinit…
In this paper, model predictive control (MPC) strategies are proposed for dead-beat control of linear systems with and without state and control constraints. In unconstrained MPC, deadbeat performance can be guaranteed by setting the control horizon to the system dimension, and adding an terminal equality constraint. It is proved that the unconstrained deadbeat MPC is equivalent to linear deadbeat control. The proposed constrained deadbeat MPC is designed by setting the control horizon equal to the system dimension and penalizing only the terminal cost. The recursive feasibility and deadbeat p…
This paper proposes an adaptive control allocation approach for uncertain over-actuated systems with actuator saturation. The proposed method does not require uncertainty estimation or a persistent excitation assumption. Using the element-wise non-symmetric projection algorithm, the adaptive parameters are restricted to satisfy certain optimality conditions leading to overall closed loop system stability. Furthermore, a sliding mode controller with a time-varying sliding surface, working in tandem with the adaptive control allocation, is proposed to guarantee the outer loop stability and refer…
UC Berkeley（加州大学伯克利分校）；Ford Research and Advanced Engineering（福特研究与高级工程部门）
We propose a Model Predictive Control (MPC) for collision avoidance between an autonomous agent and dynamic obstacles with uncertain predictions. The collision avoidance constraints are imposed by enforcing positive distance between convex sets representing the agent and the obstacles, and tractably reformulating them using Lagrange duality. This approach allows for smooth collision avoidance constraints even for polytopes, which otherwise require mixed-integer or non-smooth constraints. We consider three widely used descriptions of the uncertain obstacle position: 1) Arbitrary distribution wi…
University of Warwick（华威大学）；National University of Singapore（新加坡国立大学）；Macquarie University（麦考瑞大学）；Australian National University（澳大利亚国立大学）；Centre for Quantum Computation and Communication Technology, Australian Research Council（澳大利亚研究委员会量子计算与通信技术中心）
In this paper, we propose a chance constrained stochastic model predictive control scheme for reference tracking of distributed linear time-invariant systems with additive stochastic uncertainty. The chance constraints are reformulated analytically based on mean-variance information, where we design suitable Probabilistic Reachable Sets for constraint tightening. Furthermore, the chance constraints are proven to be satisfied in closed-loop operation. The design of an invariant set for tracking complements the controller and ensures convergence to arbitrary admissible reference points, while a …
This paper proposes a control strategy for a Reverse Fuel Cell used to manage a Renewable Energy Community. A two-stage scenario-based Model Predictive Control algorithm is designed to define the best economic strategy to be followed during operation. Renewable energy generation and users' demand are forecasted by a suitably defined Discrete Markov Chain based method. The control algorithm is able to take into account the uncertainties of forecasts and the nonlinear behaviour of the Reversible Fuel Cell. The performance of proposed approach is tested on a Renewable Energy Community composed by…
In this work, we propose a tube-based MPC scheme for state- and input-constrained linear systems subject to dynamic uncertainties characterized by dynamic integral quadratic constraints (IQCs). In particular, we extend the framework of $ρ$-hard IQCs for exponential stability analysis to external inputs. This result yields that the error between the true uncertain system and the nominal prediction model is bounded by an exponentially stable scalar system. In the proposed tube-based MPC scheme, the state of this error bounding system is predicted along with the nominal model and used as a scalin…
The H2 guaranteed cost decentralized control problem is investigated in this work. More specifically, on the basis of an appropriate H2 re-formulation that we put in place, the optimal control problem in the presence of parameter uncertainties is then suitably characterized by convex restriction and solved in parameter space. It is shown that a set of stabilizing decentralized controller gains for the uncertain system is parameterized in a convex set through appropriate convex restriction, and then an approximated conic optimization problem is constructed. This facilitates the use of the symme…
This paper studies a data-driven predictive control for a class of control-affine systems which is subject to uncertainty. With the accessibility to finite sample measurements of the uncertain variables, we aim to find controls which are feasible and provide superior performance guarantees with high probability. This results into the formulation of a stochastic optimization problem (P), which is intractable due to the unknown distribution of the uncertainty variables. By developing a distributionally robust optimization framework, we present an equivalent and yet tractable reformulation of (P)…
