Linear parameter-varying (LPV) systems with uncertainty in time-varying delays are subject to performance degradation and instability. In this line, we investigate the stability of such systems invoking an input-output stability approach. By considering explicit bounds on the delay rate and time-varying delay uncertainty, the scaled small-gain theorem is adopted to form an interconnected time-delay LPV system with input and output vectors of the auxiliary system introduced for the uncertain dynamics. For such an interconnected time-delay LPV system subject to external disturbances, a Lyapunov-Krasovskii functional (LKF) is constructed whose derivative is augmented with the terms resulted from the descriptor method. Then, stability conditions and a prescribed induced L2-norm in terms of the disturbance rejection performance are derived in a convex linear matrix inequalities (LMIs) setting. Subsequently, a congruent transformation enables us to compute a gain-scheduled state-feedback controller for a class of LPV systems with an uncertain time-varying delay. As a benchmark, we examine the automated mean arterial blood pressure (MAP) control in an individual with hypotension where the MAP response dynamics to drug infusion is characterized in a time-delay LPV representation. Finally, the closed-loop simulation results are provided to demonstrate the provided methodology's performance.
Learning Surrogate LPV State-Space Models with Uncertainty Quantification
Eindhoven University of Technology（埃因霍温理工大学）；European Space Agency, ESTEC（欧洲航天局ESTEC）；HUN-REN Institute for Computer Science and Control（HUN-REN计算机科学与控制研究所）
In this paper, we propose a learning-based Model Predictive Control (MPC) approach for the polytopic Linear Parameter-Varying (LPV) systems with inexact scheduling parameters (as exogenous signals with inexact bounds), where the Linear Time Invariant (LTI) models (vertices) captured by combinations of the scheduling parameters becomes wrong. We first propose to adopt a Moving Horizon Estimation (MHE) scheme to simultaneously estimate the convex combination vector and unmeasured states based on the observations and model matching error. To tackle the wrong LTI models used in both the MPC and MH…
Memory Resilient Gain-scheduled State-Feedback Control of Uncertain LTI/LPV Systems with Time-Varying Delays
KTH, School of Mathematics（瑞典皇家理工学院数学学院）；GIPSA-Lab, Departement of Control Systems (former LAG), Grenoble Universités, ENSE 3（格勒诺布尔大学 GIPSA 实验室控制系统系（原 LAG））；IRCCyN - Centrale de Nantes（南特中央理工学院 IRCCyN）
This paper proposes a control architecture for autonomous lane keeping by a vehicle. In this paper, the vehicle dynamics consist of two parts: lateral and longitudinal dynamics. Therefore, the control architecture comprises two subsequent controllers. A longitudinal model predictive control (MPC) makes the vehicle track the desired longitudinal speeds that are assumed to be generated by a speed planner. The longitudinal speeds are then passed to a lateral MPC for lane keeping. Due to the dependence of the lateral dynamics on the longitudinal speed, they are represented in a linear parameter-va…
In this paper, we present an effective online tube-based model predictive control (T-MPC) solution for autonomous driving that aims at improving the computational load while ensuring robust stability and performance in fast and disturbed scenarios. We focus on reformulating the non-linear original problem into a pseudo-linear problem by transforming the non-linear vehicle equations to be expressed in a Linear Parameter Varying (LPV) form. An scheme composed by a nominal controller and a corrective local controller is propossed. First, the local controller is designed as a polytopic LPV-H$_{\in…
Mean arterial blood pressure (MAP) dynamics estimation and its automated regulation could benefit the clinical and emergency resuscitation of critical patients. In order to address the variability and complexity of the MAP response of a patient to vasoactive drug infusion, a parameter-varying model with a varying time delay is considered to describe the MAP dynamics in response to drugs. The estimation of the varying parameters and the delay is performed via a Bayesian-based multiple-model square root cubature Kalman filtering approach. The estimation results validate the effectiveness of the …
This paper proposes a new Linear Fractional Transformation (LFT) modeling approach for uncertain Linear Parameter Varying (LPV) multibody systems with parameter-dependent equilibrium. Traditional multibody approaches, which consist in building the nonlinear model of the whole structure and linearizing it around equilibrium after a numerical trimming, do not allow to isolate parametric variations with the LFT form. Although additional techniques, such as polynomial fitting or symbolic linearization, can provide an LFT model, they may be time-consuming or miss worst-case configurations. The prop…
In this paper, we deal with the power regulation of tethered-wing systems and demonstrate advantages of variable-pitch control in mitigating the dynamic mechanical loads and power fluctuations. The proposed scheme is based on a strategy that maximizes the energy capture during low-speed wind and prevents overloads during the high-speed wind. To realize this strategy, we use a tether reeling-speed controller to track the optimal generator speed during low-speed wind and a MIMO speed-force controller for power limitation during high-speed wind. The controllers are synthesized using H-infinity me…
This paper presents an approach to compute the worst-case gain of the interconnection of a finite time horizon linear time-variant system and a perturbation. The input/output behavior of the uncertainty is described by integral quadratic constraints (IQCs). A condition for the worst-case gain of such an interconnection can be formulated using dissipation theory as a parameterized Riccati differential equation, which depends on the chosen IQC multiplier. A nonlinear optimization problem is formulated to minimize the upper bound of the worst-case gain over a set of admissible IQC multipliers. Th…
Stability and $L_1/\ell_1$-to-$L_1/\ell_1$ performance analysis of uncertain impulsive linear positive systems with applications to the interval observation of impulsive and switched systems with constant delays
