Embedding Constrained Model Predictive Control in a Continuous-Time Dynamic Feedback

This paper introduces a continuous-time constrained nonlinear control scheme which implements a model predictive control strategy as a continuous-time dynamic system. The approach is based on the idea that the solution of the optimal control problem can be embedded into the internal states of a dynamic control law which runs in parallel to the system. Using input to state stability arguments, it is shown that if the controller dynamics are sufficiently fast with respect to the plant dynamics, the interconnection between the two systems is asymptotically stable. Additionally, it is shown that, by augmenting the proposed scheme with an add-on unit known as an Explicit Reference Governor, it is possible to drastically increase the set of initial conditions that can be steered to the desired reference without violating the constraints. Numerical examples demonstrate the effectiveness of the proposed scheme

Constrained Control of Depth of Hypnosis During Induction Phase

This paper proposes a constrained control scheme for the control of the depth of hypnosis during induction phase in clinical anesthesia. In contrast with existing control schemes for propofol delivery, the proposed scheme guarantees overdosing prevention while ensuring good performance. The core idea is to reformulate overdosing prevention as a constraint, and then use the recently introduced Explicit Reference Governor to enforce the constraint satisfaction at all times. The proposed scheme is evaluated in comparison with a robust PID controller on a simulated surgical procedure for 44 patients whose Pharmacokinetic-Pharmacodynamic models have been identified using clinical data. The results demonstrate that the proposed constrained control scheme can deliver propofol to yield good induction phase response while preventing overdosing in patients; whereas other existing schemes might cause overdosing in some patients. Simulations show that mean rise time, mean settling time, and mean overshoot of less than 5 [min], 8 [min], and 10%, respectively, are achieved, which meet typical anesthesiologists' response specifications

Performance satisfaction in Harpy, a thruster-assisted bipedal robot

We will report our efforts in designing feedback for the thruster-assisted walking of a bipedal robot. We will assume for well-tuned supervisory controllers and will focus on fine-tuning the desired joint trajectories to satisfy the performance being sought. In doing this, we will devise an intermediary filter based on the emerging idea of reference governors. Since these modifications and impact events lead to deviations from the desired periodic orbits, we will guarantee hybrid invariance in a robust fashion by applying predictive schemes within a short time envelope during the double support phase of a gait cycle. To achieve the hybrid invariance, we will leverage the unique features in our robot, i.e., the thruster.Comment: 7 pages, accepted in American Controls Conference (ACC) 202

Safe Robot Navigation in Cluttered Environments using Invariant Ellipsoids and a Reference Governor

This paper considers the problem of safe autonomous navigation in unknown environments, relying on local obstacle sensing. We consider a control-affine nonlinear robot system subject to bounded input noise and rely on feedback linearization to determine ellipsoid output bounds on the closed-loop robot trajectory under stabilizing control. A virtual governor system is developed to adaptively track a desired navigation path, while relying on the robot trajectory bounds to slow down if safety is endangered and speed up otherwise. The main contribution is the derivation of theoretical guarantees for safe nonlinear system path-following control and its application to autonomous robot navigation in unknown environments

A Feasibility Governor for Enlarging the Region of Attraction of Linear Model Predictive Controllers

This paper proposes a method for enlarging the region of attraction of Linear Model Predictive Controllers (MPC) when tracking piecewise-constant references in the presence of pointwise-in-time constraints. It consists of an add-on unit, the Feasibility Governor (FG), that manipulates the reference command so as to ensure that the optimal control problem that underlies the MPC feedback law remains feasible. Offline polyhedral projection algorithms based on multi-objective linear programming are employed to compute the set of feasible states and reference commands. Online, the action of the FG is computed by solving a convex quadratic program. The closed-loop system is shown to satisfy constraints, be asymptotically stable, exhibit zero-offset tracking, and display finite-time convergence of the reference

Passivity based design of sliding modes for optimal Load Frequency Control

This paper proposes a distributed sliding mode control strategy for optimal Load Frequency Control (OLFC) in power networks, where besides frequency regulation also minimization of generation costs is achieved (economic dispatch). We study a nonlinear power network partitioned into control areas, where each area is modelled by an equivalent generator including voltage and second order turbine-governor dynamics. The turbine-governor dynamics suggest the design of a sliding manifold, such that the turbine-governor system enjoys a suitable passivity property, once the sliding manifold is attained. This work offers a new perspective on OLFC by means of sliding mode control, and in comparison with existing literature, we relax required dissipation conditions on the generation side and assumptions on the system parameters.Comment: 11 page

Nonlinear MPC for Tracking for a Class of Non-Convex Admissible Output Sets

This paper presents an extension to the nonlinear Model Predictive Control for Tracking scheme able to guarantee convergence even in cases of non-convex output admissible sets. This is achieved by incorporating a convexifying homeomorphism in the optimization problem, allowing it to be solved in the convex space. A novel class of non-convex sets is also defined for which a systematic procedure to construct a convexifying homeomorphism is provided. This homeomorphism is then embedded in the Model Predictive Control optimization problem in such a way that the homeomorphism is no longer required in closed form. Finally, the effectiveness of the proposed method is showcased through an illustrative example

Coupling Load-Following Control with OPF

In this paper, the optimal power flow (OPF) problem is augmented to account for the costs associated with the load-following control of a power network. Load-following control costs are expressed through the linear quadratic regulator (LQR). The power network is described by a set of nonlinear differential algebraic equations (DAEs). By linearizing the DAEs around a known equilibrium, a linearized OPF that accounts for steady-state operational constraints is formulated first. This linearized OPF is then augmented by a set of linear matrix inequalities that are algebraically equivalent to the implementation of an LQR controller. The resulting formulation, termed LQR-OPF, is a semidefinite program which furnishes optimal steady-state setpoints and an optimal feedback law to steer the system to the new steady state with minimum load-following control costs. Numerical tests demonstrate that the setpoints computed by LQR-OPF result in lower overall costs and frequency deviations compared to the setpoints of a scheme where OPF and load-following control are considered separately.Comment: This article has been accepted for publication in the IEEE Transactions on Smart Gri

Chance-Constrained Controller State and Reference Governor

The controller state and reference governor (CSRG) is an add-on scheme for nominal closed-loop systems with dynamic controllers which supervises the controller internal state and the reference input to the closed-loop system to enforce pointwise-in-time constraints. By admitting both controller state and reference modifications, the CSRG can achieve an enlarged constrained domain of attraction compared to conventional reference governor schemes where only reference modification is permitted. This paper studies the CSRG for systems subject to stochastic disturbances and chance constraints. We describe the CSRG algorithm in such a stochastic setting and analyze its theoretical properties, including chance-constraint enforcement, finite-time reference convergence, and closed-loop stability. We also present examples illustrating the application of CSRG to constrained aircraft flight control.Comment: 17 pages, 8 figure

Reference Governors for Time-varying Systems and Constraints

Control systems are often subject to constraints imposed by physical limitations or safety considerations, and require means of constraint management to ensure the stability and safety of the system. For real-time implementation, constraint management schemes must not carry a heavy computational burden; however many of the current solutions are computationally unattractive, especially those with robust formulations. Thus, the design of constraint management schemes with low computational loads is an important and practical problem for control engineers. Reference Governor (RG) is an efficient constraint management scheme that is attractive for real-time implementation due to its low computational complexity and ease of implementation. However, in theory, RG is only able to enforce constant constraints for systems with time-invariant models. In this thesis, we extend the capabilities of RG to solve two separate problems. The solution to the first problem presented in this thesis is a novel RG scheme for overshoot mitigation in tracking control systems. The proposed scheme, referred to as the Reference Governor with Dynamic Constraint (RG-DC), recasts the overshoot mitigation problem as a constraint management problem. The outcome of this reformulation is a dynamic Maximal Admissible Set (MAS), which varies in real-time as a function of the reference signal and the tracking output. RG-DC employs the dynamic MAS to modify the reference signal to mitigate or, if possible, prevent overshoot. The second solution presented in this thesis is a RG scheme for constraint management of parameter-varying systems with slowly time-varying constraints. The solution, known as the Adaptive-Contractive Reference Governor (RG-AC) utilizes a contractive characterization of MAS that changes in real-time as a function of the system\u27s time-varying parameters in a computationally attractive manner. This adaptive set is based off a first-order Taylor approximation of the parameter dependent matrices that describe the time-varying MAS. The work in this thesis is supported by simulation results which demonstrate the efficacy of both approaches, and also highlight their limitations