Output feedback control of constrained descriptor systems: a case study of a hydraulic tank system

This paper develops a framework for designing output feedback controllers for constrained linear parameter‐varying systems that experience persistent disturbances. We specifically propose an incremental parameter‐varying output feedback control law to address control rate constraints, as well as state and control amplitude constraints. This control law provides additional degrees of freedom compared to previous contributions in the literature, offering the potential for improved results in constrained control design. Our approach is based on the concept of robust positively invariant sets. We apply the extended Farkas' lemma to derive a set of algebraic conditions that define both the control gains and a robust positively invariant polyhedron that adheres to the control and state constraints. These algebraic conditions are formulated into a bilinear optimization problem, which aims to determine the output feedback gains and the associated polyhedral robust positively invariant region. The controller obtained ensures that any closed‐loop trajectory starting from the polyhedron converges to a smaller inner polyhedral set around the origin in a finite amount of time. This trajectory remains ultimately bounded, irrespective of the persistent disturbances and variations in system parameters. Furthermore, by incorporating the sizes of the two polyhedral sets into the objective function, our proposed optimization can simultaneously enlarge the outer set while minimizing the inner one. We present numerical examples and comparisons to demonstrate the effectiveness of our proposal in managing the specified constraints, disturbances, and parameter variations.

We study parametric optimal control problems governed by a system of time-dependent partial differential equations (PDE) and subject to additional control and state constraints. An approach is presented to compute the optimal control functions and the so-called sensitivity differentials of the optimal solution with respect to perturbations. This information plays an important role in the analysis of optimal solutions as well as in real-time optimal control. The method of lines is used to transform the perturbed PDE system into a large system of ordinary differential equations. A subsequent discretization then transcribes parametric ODE optimal control problems into perturbed nonlinear programming problems (NLP), which can be solved efficiently by SQP methods. Second-order sufficient conditions can be checked numerically and we propose to apply an NLP-based approach for the robust computation of the sensitivity differentials of the optimal solutions with respect to the perturbation parameters. The numerical method is illustrated by the optimal control and sensitivity analysis of the Burgers equation.

Maneuver design is a vital prerequisite for autonomy in aerospace guidance and control. It ensures system safety by analyzing the feasibility of the proposed maneuvers. This paper demonstrates a holistic approach to maneuver design by emphasizing its feasibility with consideration on the complete dynamics of the system and its constraints. Computational bifurcation analysis is employed to generate a sequence of trim solutions based on specified state and control constraints that define a stipulated maneuver. Implementing this approach on a stratospheric airship model helps attempt a few of its challenging and interesting facets like autonomous hovering, ascending, and descending by gauging its performance and formulating realistic maneuvers pertaining to the imposed limitations on the lateral excursion, control, and state constraints. The effectiveness of the proposed maneuvers is then evaluated using numerical simulations with computed control schedules in an open-loop.KeywordsStratospheric airshipManeuver designAutonomy

Feasibility and stability of constrained finite receding horizon control

The problem of explicitly determining the worst persistent input disturbance that a closed loop system can tolerate under prespecified state and control constraints is studied. Verification of designs specifically aimed at maximizing the size of persistent bounded disturbances while satisfying system constraints, typically requires extensive simulations because the exact nature of the worst input is not known. In this paper the exact nature of the worst input is completely characterized for both SISO and MIMO cases. A finite number of specific impulse responses of the closed loop system determines the worst persistent input disturbance. In the case of a SISO system with n state constraints (|x <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</sub> | ≤ ß <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</sub> ), a, control constraint (|u| ≤ ß <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">u</sub> ) and an output constraint (|y| ≤ ß <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">o</sub> ), n + 2 impulse responses are generaly needed. With this new result the large number of simulations that is typically needed for design verification can be significantly reduced. Three examples illustrate how the new characterization can be utilized.

A neural network based optimal control synthesis is presented for solving optimal control problems with control and state constraints. The optimal control problem is transcribed into nonlinear programming problem which is implemented with adaptive critic neural network. The proposed simulation methods is illustrated by the optimal control problem of feeding adaptation of filter feeders of Daphnia. Results show that adaptive critic based systematic approach holds promise for obtaining the optimal control with control and state constraints.

Controllability Analysis of Linear Time-Invariant Descriptor Systems∗∗This work was supported by CSIR, New Delhi (Grant No. 25(0195)11/EMRII).

In this paper we consider a state-constrained optimal control problem with boundary control, where the state constraints are imposed only in an interior subdomain. Our goal is to derive a priori error estimates for a finite element discretization with and without additional regularization. We will show that the separation of the set where the control acts and the set where the state constraints are given improves the approximation rates significantly. The theoretical results are illustrated by numerical computations.

The cooperative tracking control problem for the multiagent systems with unknown dynamic models, state constraints, control input constraints, optimal performance index, and convergence rate constraints is investigated in this article. A novel design framework is proposed to cope with these constraints and requirements. More specifically, the mean value theorem is utilized to transform the control input constraint to the unconstrained form. The performance function combined with a barrier Lyapunov function is leveraged to achieve the guaranteed transient tracking performance, finite-time convergence, and state constraints. To satisfy the optimal performance index, while considering the unknown dynamics of agents, we employ the actor-critic neural network architecture to get the near-optimal solution. Our control scheme is completely model-free. The rigorous Lyapunov stability analyses show that the full-state constraints and control input constraints are always satisfied, and the cooperative tracking errors can be made as small as possible in a finite time at a desired decay rate by appropriately setting the parameters in the performance function and barrier Lyapunov function. Finally, the simulation and hardware tests are conducted to clarify the effectiveness of the proposed control strategy.

Stability of Dynamic Hybrid Systems With Descriptor Systems as Dynamic Model

We discuss a linear-quadratic optimal control problem with pointwise control and state constraints. The state constraints are regularized by a Lavrentiev type regularization. The main results of the paper are estimates for the regularization error and the stability with respect to noisy data.

Considers measurement feedback switching control of systems with state and control constraints. Prior works have proved that switching control strategies have ability to resolve a common conflict in the design of state regulators such that meeting performance objectives while simultaneously avoiding violation of constraints. However, all of such switching control strategies are derived under consideration of full state feedback. In this paper, a measurement feedback switching control law is proposed. The main idea is to utilize a set-valued estimation technique which produces a set of possible state vectors consistent with measured output data. The resulting overall controller assures that state and control constraints are satisfied using only measurement feedback.

A control scheme for electrostatically shaping a membrane is developed. The scheme achieves stabilization of the first mode of the membrane at a desired equilibrium, that may be open loop unstable, without violating specified state and control constraints. The ideas on the use of an "equilibrium-parametrized" family of Lyapunov functions to enforce state and control constraints in nonlinear systems go significantly beyond the specific example treated here. They can be widely applied in the context of Lyapunov-based designs, including nonlinear systems with disturbance inputs and uncertainties.

Numerical solutions of linear time-varying descriptor systems via hybrid functions

Safe and sub-optimal CAV platoon longitudinal control protocol accounting for state constraints and uncertain vehicle dynamics