Model predictive control techniques for hybrid systems

This paper describes the main issues encountered when applying model predictive control to hybrid processes. Hybrid model predictive control (HMPC) is a research field non-fully developed with many open challenges. The paper describes some of the techniques proposed by the research community to overcome the main problems encountered. Issues related to the stability and the solution of the optimization problem are also discussed. The paper ends by describing the results of a benchmark exercise in which several HMPC schemes were applied to a solar air conditioning plant.Ministerio de Eduación y Ciencia DPI2007-66718-C04-01Ministerio de Eduación y Ciencia DPI2008-0581

Fast Non-Parametric Learning to Accelerate Mixed-Integer Programming for Online Hybrid Model Predictive Control

Today's fast linear algebra and numerical optimization tools have pushed the frontier of model predictive control (MPC) forward, to the efficient control of highly nonlinear and hybrid systems. The field of hybrid MPC has demonstrated that exact optimal control law can be computed, e.g., by mixed-integer programming (MIP) under piecewise-affine (PWA) system models. Despite the elegant theory, online solving hybrid MPC is still out of reach for many applications. We aim to speed up MIP by combining geometric insights from hybrid MPC, a simple-yet-effective learning algorithm, and MIP warm start techniques. Following a line of work in approximate explicit MPC, the proposed learning-control algorithm, LNMS, gains computational advantage over MIP at little cost and is straightforward for practitioners to implement

Predictive Control for Linear and Hybrid Systems

Model Predictive Control (MPC), the dominant advanced control approach in industry over the past twenty-five years, is presented comprehensively in this unique book. With a simple, unified approach, and with attention to real-time implementation, it covers predictive control theory including the stability, feasibility, and robustness of MPC controllers. The theory of explicit MPC, where the nonlinear optimal feedback controller can be calculated efficiently, is presented in the context of linear systems with linear constraints, switched linear systems, and, more generally, linear hybrid systems. Drawing upon years of practical experience and using numerous examples and illustrative applications, the authors discuss the techniques required to design predictive control laws, including algorithms for polyhedral manipulations, mathematical and multiparametric programming and how to validate the theoretical properties and to implement predictive control policies. The most important algorithms feature in an accompanying free online MATLAB toolbox, which allows easy access to sample solutions. Predictive Control for Linear and Hybrid Systems is an ideal reference for graduate, postgraduate and advanced control practitioners interested in theory and/or implementation aspects of predictive control

Handbook of linear data-driven predictive control:Theory, implementation and design

Data-driven predictive control (DPC) has gained an increased interest as an alternative to model predictive control in recent years, since it requires less system knowledge for implementation and reliable data is commonly available in smart engineering systems. Several data-driven predictive control algorithms have been developed recently, which largely follow similar approaches, but with specific formulations and tuning parameters. This review aims to provide a structured and accessible guide on linear data-driven predictive control methods and practices for people in both academia and the industry seeking to approach and explore this field. To do so, we first discuss standard methods, such as subspace predictive control (SPC), and data-enabled predictive control (DeePC), but we also include newer hybrid approaches to DPC, such as γ–data-driven predictive control and generalized data-driven predictive control. For all presented data-driven predictive controllers we provide a detailed analysis regarding the underlying theory, implementation details and design guidelines, including an overview of methods to guarantee closed-loop stability and promising extensions towards handling nonlinear systems. The performance of the reviewed DPC approaches is compared via simulations on two benchmark examples from the literature, allowing us to provide a comprehensive overview of the different techniques in the presence of noisy data.</p

Handbook of linear data-driven predictive control:Theory, implementation and design

Data-driven predictive control (DPC) has gained an increased interest as an alternative to model predictive control in recent years, since it requires less system knowledge for implementation and reliable data is commonly available in smart engineering systems. Several data-driven predictive control algorithms have been developed recently, which largely follow similar approaches, but with specific formulations and tuning parameters. This review aims to provide a structured and accessible guide on linear data-driven predictive control methods and practices for people in both academia and the industry seeking to approach and explore this field. To do so, we first discuss standard methods, such as subspace predictive control (SPC), and data-enabled predictive control (DeePC), but we also include newer hybrid approaches to DPC, such as γ–data-driven predictive control and generalized data-driven predictive control. For all presented data-driven predictive controllers we provide a detailed analysis regarding the underlying theory, implementation details and design guidelines, including an overview of methods to guarantee closed-loop stability and promising extensions towards handling nonlinear systems. The performance of the reviewed DPC approaches is compared via simulations on two benchmark examples from the literature, allowing us to provide a comprehensive overview of the different techniques in the presence of noisy data.</p

Approximate hybrid model predictive control for multi-contact push recovery in complex environments

Feedback control of robotic systems interacting with the environment through contacts is a central topic in legged robotics. One of the main challenges posed by this problem is the choice of a model sufficiently complex to capture the discontinuous nature of the dynamics but simple enough to allow online computations. Linear models have proved to be the most effective and reliable choice for smooth systems; we believe that piecewise affine (PWA) models represent their natural extension when contact phenomena occur. Discrete-time PWA systems have been deeply analyzed in the field of hybrid Model Predictive Control (MPC), but the straightforward application of MPC techniques to complex systems, such as a humanoid robot, leads to mixed-integer optimization problems which are not solvable at real-time rates. Explicit MPC methods can construct the entire control policy offline, but the resulting policy becomes too complex to compute for systems at the scale of a humanoid robot. In this paper we propose a novel algorithm which splits the computational burden between an offline sampling phase and a limited number of online convex optimizations, enabling the application of hybrid predictive controllers to higher-dimensional systems. In doing so we are willing to partially sacrifice feedback optimality, but we set stability of the system as an inviolable requirement. Simulation results of a simple planar humanoid that balances by making contact with its environment are presented to validate the proposed controller

Constrained anti-disturbance control for a quadrotor based on differential flatness

The classical control design based on linearised model is widely used in practice even to those inherently nonlinear systems. Although linear design techniques are relatively mature and enjoy the simple structure in implementations, they can be prone to misbehaviour and failure when the system state is far away from the operating point. To avoid the drawbacks and exploit the advantages of linear design methods while tackling the system nonlinearity, a hybrid control structure is developed in this paper. First, the model predictive control is used to impose states and inputs constraints on the linearised model, which makes the linearisation satisfy the small-perturbation requirement and reduces the bound of linearisation error. On the other hand, a combination of disturbance observer based control and H1 control, called composite hierarchical anti-disturbance control, is constructed for the linear model to provide robustness against multiple disturbances. The constrained reference states and inputs generated by the outer-loop model predictive controller are asymptotically tracked by the inner-loop composite anti-disturbance controller. To demonstrate the performance of the proposed framework, a case study on quadrotor is conducted

Robust model predictive control for dynamics compensation in real-time hybrid simulation

Hybrid simulation is an efficient method to obtain the response of an emulated system subjected to dynamic excitation by combining loading-rate-sensitive numerical and physical substructures. In such simulations, the interfaces between physical and numerical substructures are usually implemented using transfer systems, i.e., an arrangement of actuators. To guarantee high fidelity of the simulation outcome, conducting hybrid simulation in hard real-time is required. Albeit attractive, real-time hybrid simulation comes with numerous challenges, such as the inherent dynamics of the transfer system used, along with communication interrupts between numerical and physical substructures, that introduce time delays to the overall hybrid model altering the dynamic response of the system under consideration. Hence, implementation of adequate control techniques to compensate for such delays is necessary. In this study, a novel control strategy is proposed for time delay compensation of actuator dynamics in hard real-time hybrid simulation applications. The method is based on designing a transfer system controller consisting of a robust model predictive controller along with a polynomial extrapolation algorithm and a Kalman filter. This paper presents a proposed tracking controller first, followed by two virtual real-time hybrid simulation parametric case studies, which serve to validate the performance and robustness of the novel control strategy. Real-time hybrid simulation using the proposed control scheme is demonstrated to be effective for structural performance assessment

Advanced multiparametric optimization and control studies for anaesthesia

Anaesthesia is a reversible pharmacological state of the patient where hypnosis, analgesia and muscle relaxation are guaranteed and maintained throughout the surgery. Analgesics block the sensation of pain; hypnotics produce unconsciousness, while muscle relaxants prevent unwanted movement of muscle tone. Controlling the depth of anaesthesia is a very challenging task, as one has to deal with nonlinearity, inter- and intra-patient variability, multivariable characteristics, variable time delays, dynamics dependent on the hypnotic agent, model analysis variability, agent and stability issues. The modelling and automatic control of anaesthesia is believed to (i) benefit the safety of the patient undergoing surgery as side-effects may be reduced by optimizing the drug infusion rates, and (ii) support anaesthetists during critical situations by automating the drug delivery systems. In this work we have developed several advanced explicit/multi-parametric model predictive (mp-MPC) control strategies for the control of depth of anaesthesia. State estimation techniques are developed and used simultaneously with mp-MPC strategies to estimate the state of each individual patient, in an attempt to overcome the challenges of inter- and intra- patient variability, and deal with possible unmeasurable noisy outputs. Strategies to deal with the nonlinearity have been also developed including local linearization, exact linearization as well as a piece-wise linearization of the Hill curve leading to a hybrid formulation of the patient model and thereby the development of multiparametric hybrid model predictive control methodology. To deal with the inter- and intra- patient variability, as well as the noise on the process output, several robust techniques and a multiparametric moving horizon estimation technique have been design and implemented. All the studies described in the thesis are performed on clinical data for a set of 12 patients who underwent general anaesthesia.Open Acces

A learning approach to the FOM problem

Hogan recently provided an heuristic technique called family of modes (FOM) to solve model predictive control (MPC) problems under hybrid constraints and underactuation. The goal of this study is to further develop this new method and to expand its usage in the robotics manipulation community. With that objective in mind, we address some of the method's weaknesses, we provide comparison tools to try to compare the method with traditional MPC solving techniques and we provide a simple and systematic technique to set-up the method's parameters. We conclude the study by presenting our the future lines of research, which consist in generalizing the method for more complex systems and testing it's robustness.Outgoin