Robust Model Predictive Control with a Safety Mode: Applied to Small-Body Proximity Operations

Implicit improved vertex control for uncertain, time-varying linear discrete-time systems with state and control constraints

This paper addresses the issue of dealing with the asymmetric input and state constraints for robust model predictive control (RMPC) in a linear matrix inequality (LMI) framework. In order to handle the asymmetric constraints, a bias term is introduced to input and state respectively such that the symmetric constraints structures are recovered. The invariance of the shifted state is addressed and this condition is utilized for handling the shifted symmetric constraints. It is shown that the proposed approach can reduce the conservativeness of the asymmetric constraint handling in previous results. The recursive feasibility and stability of the proposed approach is guaranteed. A numerical example is shown to illustrate the effectiveness of the proposed approach.

Constant-air-volume (CAV) air-conditioning systems consist mainly of two local processes: an air-handling process and a room temperature process. A robust model predictive control (RMPC) strategy was developed for CAV air-conditioning systems, which adopted two uncertain first-order plus time-delay models to describe the dynamics of the local processes and used a linear matrix inequality (LMI)-based optimisation technique to optimise the control law. This paper develops a new control design, which reformulates the prediction models by shifting the uncertainties of the first model into the second one, and then uses the reformulated prediction models in the RMPC strategy. This paper will show that compared with the original design, the new control design can enhance the feasibility of the optimisation of control law, reduce the computational burden of the optimisation and also remove the requirement of a sensor for supply air temperature in the original design. Practical applications: The new design method is a further development of a RMPC strategy presented in Xu et al.13 It inherits the benefits of the original control design for practical application, i.e. uncertainties and constraints can be dealt with simultaneously in the design and the robustness of the controlled system can be enhanced. The new design improves the optimisation feasibility, reduces the computational complexity and does not need to measure the supply air temperature. When the new design is adopted to replace the traditional PI control, there is no necessity to change the existent input structure of the PI control. Hence, the new design can be realised in practice easier than the original design.

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

This paper addresses the trajectory optimization problem of quadrotor landing on a moving platform. Various state and control constraints are imposed, and a combined optimization objective of minimum-energy and minimum-time is considered. The contribution of the paper is to convert the original nonconvex optimal control problem into a second-order cone programming (SOCP) mainly utilizing the change of variables, equivalent transformation, and linearization. And the SOCP problem can be solved by the interior point method quickly. Then, a successive solution algorithm is proposed, which is found to be able to converge quickly. Especially, the algorithm is guaranteed to converge when the moving platform has a constant velocity vector. Numerical examples have been provided to show the efficiency and effectiveness of the proposed algorithm for quadrotor landing on moving platforms.

Vergence eye movements are essential to daily life. When driving down a highway a person typically looks between the speedometer and the road signs. This form of eye movement initiates a vergence response. Vergence is composed of convergence (inward) and divergence (outward) eye movements. Convergence movements are a combination of dual controllers, described as feedforward and feedback components. The feedforward component is a pulse of energy released by burst cells in the initial stage of the eye movement. Feedback is a series of steady periodic pulses released by tonic cells to fixate the eyes onto the target. However, divergence eye movements have not been studied extensively in the past This study will examine the neuro-control strategy used to mediate divergence eye movements (looking from near to far), when given different initial positions for the eyes to begin moving from. Preliminary data using independent component analysis (ICA) shows the divergence system contains an initial pulse, similar to the burst cells found to initiate convergence movements, when the movement began with a large initial bias (target very close to the subject). In responses beginning at a target located further away from the subject and continuing to move farther away, there is no noticeable pulse based on ICA. Demonstrated in this study is the dynamics of divergence movements at different initial conditions.

In this paper, robust constrained model predictive control of uncertain fuzzy affine systems is considered. Based on piecewise quadratic Lyapunov functions, highly efficient robust constrained predictive control approaches are developed so that the closed-loop stability is guaranteed, and the transient control performance is improved even under input or state constraints. Moreover, by using approximate ellipsoid and S -procedure, the solution to the fuzzy affine model based predictive control can be cast as a convex optimization problem subject to some linear matrix inequalities, rather than a nonconvex problem via bilinear matrix inequalities as in conventional fuzzy affine model-based control. The proposed controllers are thus easier for real-time implementation in industry. Simulation results on the fluidized bed combustion plant have demonstrated the performance of the proposed approaches.

In this paper we present a robust self-triggered model predictive control (MPC) scheme for discrete-time linear time-invariant systems subject to input and state constraints and additive disturbances. In self-triggered model predictive control, at every sampling instant an optimization problem based on the current state of the system is solved in order to determine the input applied to the system until the next sampling instant, as well as the next sampling instant itself. This leads to inter-sampling times that depend on the trajectory of the system. By maximizing the inter-sampling time, the amount of communication in the control system is reduced. In order to guarantee robust constraint satisfaction, Tube MPC methods are employed. Specifically, in order to account for the uncertainty in the system, homothetic sets are used in the prediction of the future evolution of the system. The proposed controller is shown to stabilize a closed and bounded set including the origin in its interior.

Effective recursive parallelotopic bounding for robust output-feedback 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.

In this paper, an integrated tube robust iterative learning model predictive control (Tube‐RILMPC) strategy based on the dynamic partial least squares (DyPLS) identified algorithm is proposed. The problems of large amount of online data calculation and input and output variable dimensions disaster in the original variable space are solved. This integrated Tube‐RILMPC strategy enhances the tracking performance and robustness of two‐dimensional (2D) control system. The output trajectories of system are located in the tube the nominal trajectory, which reduces the modelling error caused by the uncertain model. Based on the worst‐case performance index of ellipsoidal uncertainty and polytopic uncertainty, a robust iterative learning control (ILC) strategy is designed. Finally, the superiority of the proposed control algorithm is verified by comparative simulation.

This study presents a novel robust model predictive control (MPC) method for constrained non-linear systems with control constraints and external disturbances. The control signal is obtained by optimising an objective function consisting of two terms: an integral non-squared stage cost and a non-squared terminal cost. The terminal weighting matrix is designed appropriately such that: (i) the terminal cost serves as a control Lyapunov function; and (ii) the resultant finite horizon cost can be treated as a quasi-infinite horizon cost. Provided that the Jacobian linearisation of the system to be controlled is stabilisable and the optimisation is initially feasible, sufficient conditions ensuring the recursive feasibility of the optimisation and the robust stability of the closed-loop system are established. It is shown that the conditions rely on an appropriate design of the sampling interval with respect to a certain given disturbance level. The effectiveness of the proposed method is illustrated through a numerical example.

This paper considers a single-trajectory system identification problem for linear systems under general nonlinear and/or time-varying policies with i.i.d. random excitation noises. The problem is motivated by safe learning-based control for constrained linear systems, where the safe policies during the learning process are usually nonlinear and time-varying for satisfying the state and input constraints. In this paper, we provide a non-asymptotic error bound for least square estimation when the data trajectory is generated by any nonlinear and/or time-varying policies as long as the generated state and action trajectories are bounded. This significantly generalizes the existing non-asymptotic guarantees for linear system identification, which usually consider i.i.d. random inputs or linear policies. Interestingly, our error bound is consistent with that for linear policies with respect to the dependence on the trajectory length, system dimensions, and excitation levels. Lastly, we demonstrate the applications of our results by safe learning with robust model predictive control and provide numerical analysis.

Robustness in identification.- Comments on model validation as set membership identification.- SM identification of model sets for robust control design from data.- Robust identification and the rejection of outliers.- Semi-parametric methods for system identification.- Modal robust state estimator with deterministic specification of uncertainty.- The role of experimental conditions in model validation for control.- Modeling and validation of nonlinear feedback systems.- Towards a harmonic blending of deterministic and stochastic frameworks in information processing.- Suboptimal conditional estimators for restricted complexity set membership identification.- Worst-case simulation of uncertain systems.- On performance limitations in estimation.- Design criteria for uncertain models with structured and unstructured uncertainties.- Robustness and performance in adaptive filtering.- Nonlinear identification based on unreliable priors and data, with application to robot localization.- Robust model predictive control: A survey.- Intrinsic performance limits of linear feedback control.- Puzzles in systems and control.- Robust regional pole placement: An affine approximation.- On achieving L p (?p) performance with global internal stability for linear plants with saturating actuators.- Control under structural constraints: An input-output approach.- Multi-objective MIMO optimal control design without zero interpolation.- Robustness synthesis in l 1: A globally optimal solution.- Optimal control of distributed arrays with spatial invariance.- Numerical search of stable or unstable element in matrix or polynomial families: A unified approach to robustness analysis and stabilization.- A convex approach to a class of minimum norm problems.- Quantified inequalities and robust control.- Dynamic programming for robust control: Old ideas and recent developments.- Robustness of receding horizon control for nonlinear discrete-time systems.- Nonlinear representations and passivity conditions in discrete time.- Robust ripple-free output regulation and tracking under structured or unstructured parameter uncertainties.- An experimental study of performance and fault-tolerance of a hybrid free-flight control scheme.