Constraint Admissible Sets Research Articles

Less conservative robust reference governors and their applications

The applications of reference governors to systems with unmeasured set-bounded disturbances can lead to conservative solutions. This conservatism can be reduced by estimating the disturbance from output measurements and canceling it in the nominal control law. In this paper, a reference governor based on such an approach is considered and time-varying, disturbance and state estimation errors bounding sets are derived. Consequently, the traditional implementation of a reference governor, which exploits a constraint admissible positively-invariant set of constant commands and initial states, is replaced by one which utilizes a time-dependent sequence of similar sets (which are not necessary nested). Examples are reported which include two applications to longitudinal control of aircraft that illustrate handling of elevator uncertainty and wing icing.

Parameter-adaptive reference governors with learned robust constraint-admissible sets

Reference governors (RGs) provide an effective method for ensuring safety via constraint enforcement in closed-loop nonlinear control systems. When the system parameters are uncertain but constant, robust formulations of RGs that consider only the worst-case effect may be overly conservative and exhibit poor performance. This paper proposes a parameter-adaptive reference governor (PARG) architecture that is capable of generating safe trajectories in spite of parameter uncertainties, without being as conservative as robust RGs. The proposed approach employs machine learning on a combination of off-line simulations and on-line measurements to estimate parameter-robust constraint-admissible sets (PRCASs) that can be leveraged by the PARG. We illustrate the robust set learning and constraint enforcement qualities of the PARG using a two-dimensional electromagnetic actuator example, and further demonstrate the potential of the PARG on a vehicle case study for preventing rollover despite aggressive maneuvering.

Set-Theoretic Failure Mode Reconfiguration for Stuck Actuators

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.

Consensus of heterogeneous multi-agent system with input constraints

This work shows an approach to achieve output consensus among heterogeneous agents in a multi-agent environment where each agent is subject to input constraints. The communication among agents is described by a time-varying directed/undirected graph. The approach is based on the well-known Internal Model Principle which uses a specific class of unstable reference systems. One contribution of this work is the characterization of the maximal constraint admissible invariant set (MCAI) for the combined agent-reference system. Typically, MCAI sets do not exist for unstable systems. This work shows that for an important class of agent-reference systems that are unstable, MCAI exist and can be computed. This MCAI set is used in a novel Reference Governor, combined with a projected consensus algorithm, to achieve output consensus of all agents while satisfying constraints of each. An example is provided to illustrate the approach.

Stabilizing a multicopter using an NMPC design with a relaxed terminal region

Abstract This paper highlights the benefits of a feedback linearization local controller and the associated terminal bound constraints (box-type inequalities) in an NMPC (Nonlinear Model Predictive Control) design for a multicopter system. We replace the standard invariant construction for the terminal region of the NMPC design with two sets: i) a δ-invariant set (with δ the sampling time) which constrains the trajectories to re-enter it periodically, at pre-defined moments of time; ii) a constraint admissible safe set in which the trajectories lie in the remaining time instants. We show that this alternative construction verifies the recursive feasibility and asymptotic stability. Moreover, the additional degrees of freedom and simpler construction show advantages over similar NMPC designs with standard ellipsoidal terminal region.

Constraint admissible state sets for switched systems with average dwell time

The exact computational problem of λ-constrained admissible average dwell time (CAADT) contractive set and CAADT invariant set for discrete-time switched systems with and without persistent amplitude-bounded additive disturbance is investigated in this paper. The considered switching signal satisfies average dwell time (ADT) and is discussed in terms of stage which is both length-based and sequence-based for the first time. Two more general criteria are established for checking the existence of the λ-average dwell time (ADT) contractive set and the ADT invariant set of the considered system by assuming the value of stage length is taken from an arbitrary finite set. A detailed discussion is included to identify a proper value for stage length by taking the computational complexity and the conservatism of the designed finite-step computational algorithms of the λ-CAADT contractive set and the CAADT invariant set into consideration. Some characteristics of the admissible λ-CAADT contractive set and CAADT invariant set are derived. An illustrative example illustrates the effectiveness of the developed results.

Coordinating Controllers for Constrained Linear Systems by Virtual State Governors

We develop a method for integrating and coordinating two groups of actuators, each with a non-modifiable unconstrained state-feedback controller. The coordination strategy enforces constraints and minimizes the usage of one of the actuator groups, which is “expensive”, due to operating costs or undesired side effects. By using the maximum constraint admissible set for each controller in closed-loop with the plant, the coordination scheme modulates the action of the assigned controllers and minimizes the usage of the expensive actuators. The proposed control strategy enforces constraints, stabilizes the system, and uses the expensive actuators for finite time and only to avoid constraint violation.

Constraint-softening in model predictive control with off-line-optimized admissible sets for systems with additive and multiplicative disturbances

An approach to the softening of constraints is explored for a class of MPC algorithms that employ off-line-computed constraint-admissible sets for simplified on-line computations. The proposed approach relies on the use of exact penalty functions to ensure that the solution coincides with the actual optimal solution if the original MPC problem is feasible and that there are constraint violations at minimum possible levels if the original problem is infeasible. The approach is implemented for a class of linear systems with additive and multiplicative disturbances using a dynamic-policy-based MPC algorithm. Results specific to the cases of non-stochastic and stochastic disturbances are explored and assessed with simulation examples.

Computation of the Largest Constraint Admissible Set for Linear Continuous-Time Systems with State and Input Constraints

We present a new method for the approximation of the largest constraint admissible set (CAS) for linear continuous-time systems with state and input constraints. The CAS is the set of initial states for which the controlled system does not violate the input or state constraints. The presented approach is based on a suitable discretization of the continuous-time system. In fact, we will show that CAS in the continuous-time case can be computed analogously to the discrete-time case, given an appropriate sampling time was chosen. We stress that the computation of CAS for continuous-time systems is considerably more difficult than for discrete-time systems, since one has to guarantee that the system does not violate the constraints in between the sampling instances.

Constraint Handling in a Fuel Cell System: A Fast Reference Governor Approach

A compressor-based air supply system in a fuel cell is susceptible to saturation during transients in load. Aggressive control of the air compressor may result in compressor surge or choke, disrupt the flow of air into the cathode of a fuel cell stack, and negatively impact the fuel cell power generation. Low partial oxygen pressure in the cathode caused by rapid increase in load may also damage the stack and reduce its life. A load governor can be added to the air supply control system to monitor the load and prevent violation of constraints (compressor surge, choke, and partial oxygen pressure) by modifying the load command to the fuel cell system. In this paper, we present the steps involved in the design of such a load governor for the fuel cell application. To reduce the online computations, we utilize the fast reference governor (FRG) approach which has been developed for linear systems. FRG utilize a maximal constraint admissible set calculated offline and, thus, require fewer online calculations. We propose a modification to the FRG design to make it applicable to the nonlinear fuel cell plant. The scheme is then implemented on a real-time simulation platform and it is shown that the computations of the load governor can be performed in real-time