Set-Theoretic Failure Mode Reconfiguration for Stuck Actuators

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.

The reference governor is an add-on scheme to a pre-stabilized system that enforces pointwise-in-time state and control constraints. It does so by monitoring and minimally adjusting the reference command to ensure system response to the adjusted reference satisfies prescribed constraints. Conventional approaches to reference governor design rely on explicit models of the system. In this paper, we propose a reference governor approach for systems that admit only implicit models and are subject to set-bounded disturbance inputs. To ensure constraint satisfaction in the presence of uncertain but set-bounded disturbances, the proposed reference governor exploits metric regularity, a tool from variational analysis. We illustrate the effectiveness and online feasibility of the proposed reference governor approach through a power system example.

This paper proposes a Failure Mode and Effect Management (FMEM) strategy for constrained systems with redundant actuators based on the combined use of constraint admissible and recoverable sets. Several approaches to ensure reconfiguration of the system without constraint violation in the event of actuator failures are presented. Numerical simulation results are reported.

Less conservative robust reference governors and their applications

A set-theoretic Failure Model and Effect Management (FMEM) strategy for stuck/jammed actuators in systems with redundant actuators is considered. This strategy uses a reference governor for command tracking while satisfying state and control constraints and, once the failure mode is known, generates a recovery command sequence during mode transitions triggered by actuator failures. In the paper, this FMEM strategy is enhanced with a scheme to detect and isolate failures within a finite time, and to handle unmeasured set-bounded disturbance inputs. A numerical example is reported to illustrate the offline design process and the online operation with the proposed approach.

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

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.

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.

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.

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.

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.

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.

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.