Robust Reference Governor for Implicit Systems Using the Metric Regularity

Reference governors enforce pointwise-in-time state and control constraints by temporarily modifying the reference command to a nominal closed-loop system whenever the danger of constraint violation exists. In this paper we propose a reference governor with the added capability of resetting internal closed-loop system states as necessary to avoid constraint violation. With this approach the constrained domain of attraction, i.e., the set of states recoverable without constraint violation, is enlarged. This scheme is referred to as the controller state and reference governor. The paper describes this scheme, analyzes its stability and convergence properties, and presents examples of applying it to aircraft flight control and gas turbine engine control examples.

Proposes an approach to reference governor design. As in the prior literature, the governor accepts input commands and modifies their evolution so that specified pointwise-in-time constraints on state and control variables are satisfied. The new approach has several important advantages: it applies to continuous-time nonlinear systems, the design process is based on families of Lyapunov functions, the governor has a relatively simple implementation, the underlying theory is simple and self-contained. Key issues related to reference governor implementation are discussed in a general way, including the description of hybrid reference governors that allow the set of command inputs to be nonconvex.

In this paper we present an approach for designing of reference tracking controllers for constrained, discrete-time piecewise affine systems. The approach follows the idea of reference governor techniques where the desired set-point is filtered by a system called the “reference governor”. Based on the system current state, set-point, and prescribed constraints, the reference governor computes a new set-point for a low-level controller so that the state and input constraints are satisfied and convergence to the original set-point is guaranteed.

This paper presents a novel reference-governor-based approach to enforcing constraints in open-loop systems, where the constraint enforcement scheme modifies a control signal from a feedback controller. The reference governor is not typically applicable to these systems, since reference governors modify reference signals, which are inputs to a feedback controller.The design is based on duplicating the feedback controller of the closed-loop system and implementing a reference governor to modify the reference input to the duplicate controller. Effectively, this bypasses the nominal controller, whose internal dynamics may not be asymptotically stable. We present a method to ensure stability of the closed-loop system by ceding some control authority to the nominal controller.A numerical example is considered in which the nominal controller is a human operator of a steer-by-wire system. The operator is modeled as a PID controller with unknown parameters. Results show that the inner-loop governor design is able to satisfactorily enforce constraints in such an application.

This paper describes a learning-based approach to operating safety-critical control systems. A reference governor is an add-on scheme used to guard the nominal system against violation of pre-specified constraints by modifying set-point commands. A learning algorithm is developed in this paper to evolve the reference governor parametrization to gradually improve its performance in terms of response speed. In particular, the learning algorithm does not rely on an explicit model of the control system, i.e., it is model-free, and guarantees constraint satisfaction for all time, both during and after learning. The approach is applied to a case study of ground vehicle rollover avoidance to illustrate its functionality and characteristics.

This letter proposes a set-theoretic Failure Mode and Effect Management (FMEM) strategy that handles stuck/jammed actuators and enforces pointwise-in-time state and control constraints. The approach exploits nesting between constraint admissible and recoverable sets to ensure the existence of a recovery sequence. A reference governor is applied to track reference commands while imposing constraint satisfaction using the remaining working actuators. Numerical results of an aircraft longitudinal flight application are reported.

This paper proposes a new formulation for the Reference Governor (RG) applied to linear systems affected by exogenous disturbances, specifically those large enough to cause constraint violation. This formulation is based on a set-theoretic approach which includes external disturbances within a new RG, that we call Recovery RG (RRG). The idea is to update the Maximal Output Admissible Set (MAS) and compute a constraint-admissible input that recovers the system from constraint violation at steady-state. The proposed RRG overcomes some of the limitations of standard RG schemes, and maintains their desirable features such as formulation simplicity and finite time determination of the MAS. We validate this new scheme by simulating a linearized turbocharged gasoline engine affected by additive disturbances.

In a quick motion system, the shortest setting time is usually pursued, while for a system existing both input constraint and state constraints, by using traditional reference governor, maybe there are one phenomenon: some state don't achieve maximal valve due to shape of invariant set, This will lead to a longer setting time. This paper provides a method to shorten setting time of output via an outer feedback based on traditional reference governor. Outer feedback is computed by solving a convex non-constrained quadratic optimization. For linear system with outer feedback, different invariant set is computed based on reference governor. Meanwhile, this paper describes a built process of serval invariant sets and provides a most big invariant set just to fulfill the first receding horizon to get the shortest setting time.

This paper presents a constraint management strategy based on Scalar Reference Governors (SRG) to enforce output, state, and control constraints while taking into account the preview information of the reference signals. The strategy, referred to as the Preview Reference Governor (PRG), can outperform SRG while maintaining the highly-attractive computational benefits of SRG. However, as it is shown, the performance of PRG may suffer if large preview horizons are used. An extension of PRG, referred to as Multi-horizon PRG, is proposed to remedy this issue. Quantitative comparisons between SRG, PRG, and Multi-horizon PRG on a vehicle rollover example are presented to illustrate their performance and computation time.

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

In the setting of discrete-time linear systems with unmeasured set-bounded disturbances, this paper proposes a control scheme that combines a disturbance free input-constrained Model Predictive Control (uMPC) policy and a reference governor (RG) which modifies the reference command to enforce constraints that are not enforced by the uMPC policy. Such a scheme, referred to as the robust RGMPC, can handle (possibly nonlinear) state and input constraints and only requires solving an optimisation problem for MPC with polytopic input constraints, for which fast algorithms exist. Conditions are given which ensure recursive feasibility of the robust RGMPC scheme, finite-time convergence of the modified reference command to the desired reference command and asymptotic convergence of the state to an invariant neighbourhood of the associated set-point. Simulation results for a constrained spacecraft rendezvous manoeuvre demonstrate that the rRGMPC scheme has lower average computational time than several robust state and input-constrained MPC controllers.

Less conservative robust reference governors and their applications

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.

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.