Model Predictive Control meets robust Kalman filtering

Model Predictive Control (MPC) is the principal control technique used in industrial applications. Although it offers distinguishable qualities that make it ideal for industrial applications, it can be questioned its robustness regarding model uncertainties and external noises. In this paper we propose a robust MPC controller that merges the simplicity in the design of MPC with added robustness. In particular, our control system stems from the idea of adding robustness in the prediction phase of the algorithm through a specific robust Kalman filter recently introduced. Notably, the overall result is an algorithm very similar to classic MPC but that also provides the user with the possibility to tune the robustness of the control. To test the ability of the controller to deal with errors in modeling, we consider a servomechanism system characterized by nonlinear dynamics

Reference tracking stochastic model predictive control over unreliable channels and bounded control actions

A stochastic model predictive control framework over unreliable Bernoulli communication channels, in the presence of unbounded process noise and under bounded control inputs, is presented for tracking a reference signal. The data losses in the control channel are compensated by a carefully designed transmission protocol, and that of the sensor channel by a dropout compensator. A class of saturated, disturbance feedback policies is proposed for control in the presence of noisy dropout compensation. A reference governor is employed to generate trackable reference trajectories and stability constraints are employed to ensure mean-square boundedness of the reference tracking error. The overall approach yields a computationally tractable quadratic program, which can be iteratively solved online

Offset-free receding horizon control of constrained linear systems

The design of a dynamic state feedback receding horizon controller is addressed, which guarantees robust constraint satisfaction, robust stability and offset-firee control of constrained linear systems in the presence of time-varying setpoints and unmeasured disturbances. This objective is obtained by first designing a dynamic linear offset-free controller and computing an appropriate domain of attraction for this controller. The linear (unconstrained) controller is then modified by adding a perturbation term, which is computed by a (constrained) robust receding horizon controller. The receding horizon controller has the property that its domain of attraction contains that of the linear controller. In order to ensure robust constraint satisfaction, in addition to offset-free control, the transient, as well as the limiting behavior of the disturbance and setpoint need to be taken into account in the design of the receding horizon controller. The fundamental difference between the results and the existing literature on receding horizon control is that the transient effect of the disturbance and set point sequences on the so-called "target calculator" is explicitly incorporated in the formulation of the receding horizon controller. An example of the control of a continuous stirred-tank reactor is presented. (c) 2005 American Institute of Chemical Engineers

Online learning with stability guarantees: A memory-based real-time model predictive controller

We propose and analyze a real-time model predictive control (MPC) scheme that utilizes stored data to improve its performance by learning the value function online with stability guarantees. For linear and nonlinear systems, a learning method is presented that makes use of basic analytic properties of the cost function and is proven to learn the MPC control law and the value function on the limit set of the closed-loop state trajectory. The main idea is to generate a smart warm start based on historical data that improves future data points and thus future warm starts. We show that these warm starts are asymptotically exact and converge to the solution of the MPC optimization problem. Thereby, the suboptimality of the applied control input resulting from the real-time requirements vanishes over time. Simulative examples show that existing real-time MPC schemes can be improved by storing data and the proposed learning scheme.Comment: This article is an extended version of the paper "Online learning with stability guarantees: A memory-based warm starting for real-time MPC" published in Automatica, Volume 122, 109247, 2020, including all proofs, an application example, and a detailed description of the used algorith

Fulfilling hard constraints in uncertain linear systems by reference managing

A method based on conceptual tools of predictive control is described for tackling tracking problems of uncertain linear systems wherein pointwise-in-time input and/or state inequality constraints are present. The method consists of adding to a primal compensated system a nonlinear device called predictive reference filter which manipulates the desired reference in order to fulfill the prescribed constraints. Provided that an admissibility condition on the initial state is satisfied, the control scheme is proved to fulfill the constraints, as well as stability and set-point tracking requirements, for all systems whose impulse/step responses lie within given uncertainty ranges

Development of robust building energy demand-side control strategy under uncertainty

The potential of carbon emission regulations applied to an individual building will encourage building owners to purchase utility-provided green power or to employ onsite renewable energy generation. As both cases are based on intermittent renewable energy sources, demand side control is a fundamental precondition for maximizing the effectiveness of using renewable energy sources. Such control leads to a reduction in peak demand and/or in energy demand variability, therefore, such reduction in the demand profile eventually enhances the efficiency of an erratic supply of renewable energy. The combined operation of active thermal energy storage and passive building thermal mass has shown substantial improvement in demand-side control performance when compared to current state-of-the-art demand-side control measures. Specifically, "model-based" optimal control for this operation has the potential to significantly increase performance and bring economic advantages. However, due to the uncertainty in certain operating conditions in the field its control effectiveness could be diminished and/or seriously damaged, which results in poor performance. This dissertation pursues improvements of current demand-side controls under uncertainty by proposing a robust supervisory demand-side control strategy that is designed to be immune from uncertainty and perform consistently under uncertain conditions. Uniqueness and superiority of the proposed robust demand-side controls are found as below: a. It is developed based on fundamental studies about uncertainty and a systematic approach to uncertainty analysis. b. It reduces variability of performance under varied conditions, and thus avoids the worst case scenario. c. It is reactive in cases of critical "discrepancies" observed caused by the unpredictable uncertainty that typically scenario uncertainty imposes, and thus it increases control efficiency. This is obtainable by means of i) multi-source composition of weather forecasts including both historical archive and online sources and ii) adaptive Multiple model-based controls (MMC) to mitigate detrimental impacts of varying scenario uncertainties. The proposed robust demand-side control strategy verifies its outstanding demand-side control performance in varied and non-indigenous conditions compared to the existing control strategies including deterministic optimal controls. This result reemphasizes importance of the demand-side control for a building in the global carbon economy. It also demonstrates a capability of risk management of the proposed robust demand-side controls in highly uncertain situations, which eventually attains the maximum benefit in both theoretical and practical perspectives.Ph.D.Committee Chair: Augenbroe, Gofried; Committee Member: Brown, Jason; Committee Member: Jeter, Sheldon; Committee Member: Paredis,Christiaan; Committee Member: Sastry, Chellur

Variational and Time-Distributed Methods for Real-time Model Predictive Control

This dissertation concerns the theoretical, algorithmic, and practical aspects of solving optimal control problems (OCPs) in real-time. The topic is motivated by Model Predictive Control (MPC), a powerful control technique for constrained, nonlinear systems that computes control actions by solving a parameterized OCP at each sampling instant. To successfully implement MPC, these parameterized OCPs need to be solved in real-time. This is a significant challenge for systems with fast dynamics and/or limited onboard computing power and is often the largest barrier to the deployment of MPC controllers. The contributions of this dissertation are as follows. First, I present a system theoretic analysis of Time-distributed Optimization (TDO) in Model Predictive Control. When implemented using TDO, an MPC controller distributed optimization iterates over time by maintaining a running solution estimate for the optimal control problem and updating it at each sampling instant. The resulting controller can be viewed as a dynamic compensator which is placed in closed-loop with the plant. The resulting coupled plant-optimizer system is analyzed using input-to-state stability concepts and sufficient conditions for stability and constraint satisfaction are derived. When applied to time distributed sequential quadratic programming, the framework significantly extends the existing theoretical analysis for the real-time iteration scheme. Numerical simulations are presented that demonstrate the effectiveness of the scheme. Second, I present the Proximally Stabilized Fischer-Burmeister (FBstab) algorithm for convex quadratic programming. FBstab is a novel algorithm that synergistically combines the proximal point algorithm with a primal-dual semismooth Newton-type method. FBstab is numerically robust, easy to warmstart, handles degenerate primal-dual solutions, detects infeasibility/unboundedness and requires only that the Hessian matrix be positive semidefinite. The chapter outlines the algorithm, provides convergence and convergence rate proofs, and reports some numerical results from model predictive control benchmarks and from the Maros-Meszaros test set. Overall, FBstab shown to be is competitive with state of the art methods and to be especially promising for model predictive control and other parameterized problems. Finally, I present an experimental application of some of the approaches from the first two chapters: Emissions oriented supervisory model predictive control (SMPC) of a diesel engine. The control objective is to reduce engine-out cumulative NOx and total hydrocarbon (THC) emissions. This is accomplished using an MPC controller which minimizes deviation from optimal setpoints, subject to combustion quality constraints, by coordinating the fuel input and the EGR rate target provided to an inner-loop airpath controller. The SMPC controller is implemented using TDO and a variant of FBstab which allows us to achieve sub-millisecond controller execution times. We experimentally demonstrate 10-15% cumulative emissions reductions over the Worldwide Harmonized Light Vehicles Test Cycle (WLTC) drivecycle.PHDAerospace EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/155167/1/dliaomcp_1.pd

Robust constraint satisfaction: invariant sets and predictive control

Set invariance plays a fundamental role in the design of control systems for constrained systems sincethe constraints can be satisfied for all time if and only if the initial state is contained inside an invariantset. This thesis is concerned with robust set invariance theory and its application to guaranteeingfeasibility in model predictive control.In the first part of this thesis, some of the main ideas in set invariance theory are brought togetherand placed in a general, nonlinear setting. The key ingredients in computing robust controllable andinvariant sets are identified and discussed. Following this, linear systems with parametric uncertaintyand state disturbances are considered and algorithms for computing the respective robust controllableand invariant sets are described. In addition to discussing linear systems, an algorithm for computingthe robust controllable sets for piecewise affine systems with state disturbances is described.In the second part, the ideas from set invariance are applied to the problem of guaranteeing feasibilityand robust constraint satisfaction in Model Predictive Control (MPC). A new sufficient condition isderived for guaranteeing feasibility of a given MPC scheme. The effect of the choice of horizons andconstraints on the feasible set of the MPC controller is also investigated. Following this, a necessaryand sufficient condition is derived for determining whether a given MPC controller is robustly feasible.The use of a robustness constraint for designing robust MPC controllers is discussed and it is shownhow this proposed scheme can be used to guarantee robust constraint satisfaction for linear systemswith parametric uncertainty and state disturbances. A new necessary and sufficient condition as wellas some new sufficient conditions are derived for guaranteeing that the proposed MPC scheme isrobustly feasible.The third part of this thesis is concerned with recovering from constraint violations. An algorithm ispresented for designing soft-constrained MPC controllers which guarantee constraint satisfaction, ifpossible. Finally, a mixed-integer programming approach is described for finding a solution whichminimises the number of violations in a set of prioritised constraints