Robust Constrained Model Predictive Control using Linear Matrix Inequalities

The primary disadvantage of current design techniques for model predictive control (MPC) is their inability to deal explicitly with plant model uncertainty. In this paper, we present a new approach for robust MPC synthesis which allows explicit incorporation of the description of plant uncertainty in the problem formulation. The uncertainty is expressed both in the time domain and the frequency domain. The goal is to design, at each time step, a state-feedback control law which minimizes a "worst-case" infinite horizon objective function, subject to constraints on the control input and plant output. Using standard techniques, the problem of minimizing an upper bound on the "worst-case" objective function, subject to input and output constraints, is reduced to a convex optimization involving linear matrix inequalities (LMIs). It is shown that the feasible receding horizon state-feedback control design robustly stabilizes the set of uncertain plants under consideration. Several extensions, such as application to systems with time-delays and problems involving constant set-point tracking, trajectory tracking and disturbance rejection, which follow naturally from our formulation, are discussed. The controller design procedure is illustrated with two examples. Finally, conclusions are presented

Anti-Windup Design for Internal Model Control

This paper considers linear control design for systems with input magnitude saturation. A general anti-windup scheme which optimizes nonlinear performance, applicable to MIMO systems, is developed. Several examples, including an ill-conditioned plant, show that the scheme provides graceful degradation of performance. The attractive features of this scheme are its simplicity and effectiveness

A Unified Framework for the Study of Anti-Windup Designs

We present a unified framework for the study of linear time-invariant (LTI) systems subject to control input nonlinearities. The framework is based on the following two-step design paradigm: "Design the linear controller ignoring control input nonlinearities and then add anti-windup bumpless transfer (AWBT) compensation to minimize the adverse eflects of any control input nonlinearities on closed loop performance". The resulting AWBT compensation is applicable to multivariable controllers of arbitrary structure and order. All known LTI anti-windup and/or bumpless transfer compensation schemes are shown to be special cases of this framework. It is shown how this framework can handle standard issues such as the analysis of stability and performance with or without uncertainties in the plant model. The actual analysis of stability and performance, and robustness issues are problems in their own right and hence not detailed here. The main result is the unification of existing schemes for AWBT compensation under a general framework

Data Driven Control of Vagus Nerve Stimulation for the Cardiovascular System: An in Silico Computational Study

Vagus nerve stimulation is an emerging therapy that seeks to offset pathological conditions by electrically stimulating the vagus nerve through cuff electrodes, where an electrical pulse is defined by several parameters such as pulse amplitude, pulse width, and pulse frequency. Currently, vagus nerve stimulation is under investigation for the treatment of heart failure, cardiac arrhythmia and hypertension. Through several clinical trials that sought to assess vagus nerve stimulation for the treatment of heart failure, stimulation parameters were determined heuristically and the results were inconclusive, which has led to the suggestion of using a closed-loop approach to optimize the stimulation parameters. A recent investigation has demonstrated highly specific control of cardiovascular physiology by selectively activating different fibers in the vagus nerve. When multiple locations and multiple stimulation parameters are considered for optimization, the design of closed-loop control becomes considerably more challenging. To address this challenge, we investigated a data-driven control scheme for both modeling and controlling the rat cardiovascular system. Using an existing in silico physiological model of a rat heart to generate synthetic input-output data, we trained a long short-term memory network (LSTM) to map the effect of stimulation on the heart rate and blood pressure. The trained LSTM was utilized in a model predictive control framework to optimize the vagus nerve stimulation parameters for set point tracking of the heart rate and the blood pressure in closed-loop simulations. Additionally, we altered the underlying in silico physiological model to consider intra-patient variability, and diseased dynamics from increased sympathetic tone in designing closed-loop VNS strategies. Throughout the different simulation scenarios, we leveraged the design of the controller to demonstrate alternative clinical objectives. Our results show that the controller can optimize stimulation parameters to achieve set-point tracking with nominal offset while remaining computationally efficient. Furthermore, we show a controller formulation that compensates for mismatch due to intra-patient variabilty, and diseased dynamics. This study demonstrates the first application and a proof-of-concept for using a purely data-driven approach for the optimization of vagus nerve stimulation parameters in closed-loop control of the cardiovascular system

Controlling neocortical epileptic seizures using forced temporal spike-time stimulation: an in silico computational study

Epileptic seizure is typically characterized by highly synchronized episodes of neural activity. Existing stimulation therapies focus purely on suppressing the pathologically synchronized neuronal firing patterns during the ictal (seizure) period. While these strategies are effective in suppressing seizures when they occur, they fail to prevent the re-emergence of seizures once the stimulation is turned off. Previously, we developed a novel neurostimulation motif, which we refer to as “Forced Temporal Spike-Time Stimulation” (FTSTS) that has shown remarkable promise in long-lasting desynchronization of excessively synchronized neuronal firing patterns by harnessing synaptic plasticity. In this paper, we build upon this prior work by optimizing the parameters of the FTSTS protocol in order to efficiently desynchronize the pathologically synchronous neuronal firing patterns that occur during epileptic seizures using a recently published computational model of neocortical-onset seizures. We show that the FTSTS protocol applied during the ictal period can modify the excitatory-to-inhibitory synaptic weight in order to effectively desynchronize the pathological neuronal firing patterns even after the ictal period. Our investigation opens the door to a possible new neurostimulation therapy for epilepsy

CONTROL-CORE: A Framework for Simulation and Design of Closed-Loop Peripheral Neuromodulation Control Systems

Closed-loop Vagus Nerve Stimulation (VNS) based on physiological feedback signals is a promising approach to regulate organ functions and develop therapeutic devices. Designing closed-loop neurostimulation systems requires simulation environments and computing infrastructures that support i) modeling the physiological responses of organs under neuromodulation, also known as physiological models, and ii) the interaction between the physiological models and the neuromodulation control algorithms. However, existing simulation platforms do not support closed-loop VNS control systems modeling without extensive rewriting of computer code and manual deployment and configuration of programs. The CONTROL-CORE project aims to develop a flexible software platform for designing and implementing closed-loop VNS systems. This paper proposes the software architecture and the elements of the CONTROL-CORE platform that allow the interaction between a controller and a physiological model in feedback. CONTROL-CORE facilitates modular simulation and deployment of closed-loop peripheral neuromodulation control systems, spanning multiple organizations securely and concurrently. CONTROL-CORE allows simulations to run on different operating systems, be developed in various programming languages (such as Matlab, Python, C++, and Verilog), and be run locally, in containers, and in a distributed fashion. The CONTROL-CORE platform allows users to create tools and testbenches to facilitate sophisticated simulation experiments. We tested the CONTROL-CORE platform in the context of closed-loop control of cardiac physiological models, including pulsatile and nonpulsatile rat models. These were tested using various controllers such as Model Predictive Control and Long-Short-Term Memory based controllers. Our wide range of use cases and evaluations show the performance, flexibility, and usability of the CONTROL-CORE platform

Control of Systems Subject to Constraints

Every operating control system must deal with constraints. On the one hand, the range and rate of change of the input or manipulated variable is limited by the physical nature of the actuator (saturation limits). On the other hand, process state variables or outputs (pressures, temperatures, voltages) may not be allowed to exceed certain bounds arising from equipment limitation, safety considerations, or environmental regulations. A rich theory exists for designing controllers - both linear (H2/H∞, LQG, LTR, pole-placement) and nonlinear (nonlinear H∞, control, feedback linearization, sliding mode control, gain scheduling). However, none of these popular and fashionable controller design techniques account for the presence of input or output constraints. Although occasionally these constraints may be neglected, in general, they lead to design and operating problems unless they are accounted for properly. In traditional control practice, overrides or mode selection schemes are used to deal with output constraints: they switch between a "bank" of controllers, each of which is designed to achieve a specific objective. In both cases (saturation limit and mode selection), a control input nonlinearity is introduced into the operating system. Despite its significance, the study of the constrained control problem has received far less attention than the traditional unconstrained (linear and nonlinear) control theory. With few exceptions, most of the controller design techniques for constrained systems are by-and-large ad-hoc, with very little guarantees of stability, performance and robustness to plant model uncertainty. The objective of this thesis is to take a broad approach towards the constrained control problem. One part of the thesis is devoted to the development of a systematic and unifying theory for studying the so-called Anti-Windup Bumpless Transfer (AWBT) problem. The other part aims towards the development of a general novel approach for the synthesis of a robust model predictive control (MPC) algorithm.</p