Learning affine predictors for MPC of nonlinear systems via artificial neural networks

The paper considers formulations of constrained model predictive control (MPC) problems for systems with dynamics defined on smooth manifolds. Generalizations of conventional nonlinear MPC stabilization techniques based on the terminal set and terminal penalty approaches are presented based on recent work by the authors. The significance of the results includes the possibility of systematically generating globally stabilizing, discontinuous, time-invariant feedback laws in situations when smooth, or even continuous, globally stabilizing, time-invariant stabilizers do not exist. To illustrate the development of nonlinear MPC on manifolds, the paper considers an example of a system with dynamics evolving on SE(3). Such systems emerge in many applications, such as quadrotor and quadcopter flight control. In the example, the paper demonstrates semi-global stabilization properties of the nonlinear MPC feedback law.

Numerical Methods for Solution of the Extended Linear Quadratic Control Problem

In this study, a collision avoidance method with model predictive control is proposed for a nonlinear model of a four-wheeled vehicle. The C/GMRES algorithm is used for solving the nonlinear model predictive control (NMPC) problem within a short sampling period. A nonlinear tire model is employed to represent the realistic behavior of a vehicle. Here, to consider whether it is possible to avoid an obstacle physically, an unavoidable region (UR) is constructed as the region in which the vehicle cannot avoid the obstacle owing to physical limitations. Even if the distance between the vehicle and the obstacle is short, the vehicle is controlled by NMPC not only to avoid the UR but also to stay on the road. A performance index for satisfying the above constraints is proposed, and control responses are investigated through numerical simulations.

This paper deals with the application of interval arithmetic to non linear model predictive control (NMPC) problem. The NMPC problem is expressed as a constraints satisfaction problem (CSP) which can be solved by interval analysis techniques. We present the classical interval techniques to build a nonlinear model predictive control law and propose some improvements in order to adapt interval tools to the context of control. Moreover, in order to reduce the pessimism introduced by interval state estimation, we propose a spatial discretisation of the input. These methods are illustrated on a inverted pendulum model.

In the model predictive control (MPC) framework a controller is computed using a finite horizon optimal control cost. When linear constraints are imposed on the system with a quadratic cost function, then the MPC problem can be reformulated as a constrained quadratic programming (QP) problem. In this paper active set methods are used in order to solve the QP problem associated with MPC, and it is shown that it is possible to use information from the previous sample interval in order to provide improved initial conditions for the QP problem which is applied to the subsequent sample interval. Simulations show that when real-time considerations force the used of suboptimal intermediate control values, then improved initial conditions can allow for control values which are closer to the true optimal solution than obtained when using standard initial conditions. These ideas can allow for the implementation of MPC schemes on a greater number of real industrial applications, where standard MPC control cannot be applied due to the excessive CPU time requirements

NONLINEAR MODEL PREDICTIVE CONTROL BASED ON SEQUENTIAL MONTE CARLO STATE ESTIMATION

Model predictive control (MPC) techniques are considered for industrial centrifugal compression systems with nonlinear dynamics, to address process and antisurge control for reaching the desired pressure ratio and surge distance. We consider a contractive nonlinear MPC formulation that ensures asymptotic stability of the closed-loop system by imposing the decrease of a quadratic Lyapunov function via an additional constraint. We discuss recursive feasibility and estimate the region of attraction via numerical methods. We also consider alternative MPC formulations, including offset-free linear and nonlinear MPC to handle the effects of disturbances and unmodeled dynamics. The computational efficiency of an approximation based on sequential quadratic programming (SQP), that yields a closed-loop performance comparable to the full nonlinear MPC is also discussed. All of the controllers considered are tested in simulations that emulate a realistic test bench and their computational time is assessed on an industrial Programmable Logic Controller (PLC). Their performance is compared with standard industrial control in nominal and perturbed cases replicating the typical and critical disturbances and model mismatches. The numerical results show that the SQP and nonlinear MPC methods outperform the other controllers in the considered scenarios, based on closed-loop performance metrics for the surge margin, the reference tracking accuracy, and the system actuation, without significantly increasing the computational time.

This paper describes a receding-horizon optimal control scheme for autonomous trajectory generation and flight control of an unmanned air vehicle in urban terrain. In such environments, the mission objective or terrain may be dynamic, and the vehicle may change dynamics mid-flight due to sensor or actuator failure; thus off-line pre-planned flight trajectories axe limiting and insufficient. This technology is aimed at supporting guidance and control for future missions that will require vehicles with increased autonomy in dangerous situations and with tight maneuvering and operational capability e.g., missions in urban environments. A Model Predictive Control (MPC) scheme is described here that navigates a vehicle with nonlinear dynamics through a vector of known way-points to a goal, and manages constraints. In this MPC-based approach to trajectory planning with constraints, a feedforward nominal trajectory is used to convert the nonconvex, nonlinear optimal control problem into a time-varying linear, convex optimization or quadratic programming problem. The nonconvex, admissible path space is converted to a sequence of overlapping, convex spaces. The feedforward control that produces the nominal trajectory is found from the vehicle's differentially flat outputs. MPC is used to determine the optimal perturbations to the nominal control that will suitably navigate the vehicle through a constrained input/output space while minimizing actuation effort. Simulation results with a non-real-time, online MPC controller for a UAV in a planar urban terrain are included to support the proposed approach.

In this paper we investigate the use of optimal control techniques to improve Functional Electrical Stimulation (FES) for drop foot correction on hemiplegic patients. A model of the foot and the tibialis anterior muscle, the contraction of which is controlled by electrical stimulation has been established and is used in the optimal control problem. The novelty in this work is the use of the ankle accelerations and shank orientations (so-called external states) in the model, which have been measured on hemiplegic patients in a previous experiment using Inertial Measurement Units (IMUs). The optimal control problem minimizes the square of muscle excitations which serves the overall goal of reducing energy consumption in the muscle. In a first step, an offline optimal control problem is solved for test purposes and shows the efficiency of the FES optimal control for drop foot correction. In a second step, a Nonlinear Model Predictive Control (NMPC) problem - or online optimal control problem, is solved in a simulated environment. While the ulitmate goal is to use NMPC on the real system, i.e. directly on the patient, this test in simulation was meant to show the feasibility of NMPC for online drop foot correction. In the optimization problem, a set of fixed constraints of foot orientation was applied. Then, an original adaptive constraint taking into account the current ankle height, was introduced and tested. Comparisons between results under fixed and adaptive constraints highlight the advantage of the adaptive constraints in terms of energy consumption, where its quadratic sum of controls, obtained by NMPC, was three times lower than with the fixed constraint. This feasibility study was a first step in application of NMPC on real hemiplegic patients for online FES-based drop foot correction. The adaptive constraints method presents a new and efficient approach in terms of muscular energy consumption minimization.

ABSTRACTThis paper presents a nonlinear model predictive control (MPC) formulation for obstacle avoidance in high-speed, large-size autono-mous ground vehicles (AGVs) with high centre of gravity (CoG) that operate in unstructured environments, such as military vehicles. The term ‘unstructured’ in this context denotes that there are no lanes or traffic rules to follow. Existing MPC formulations for passenger vehicles in structured environments do not readily apply to this context. Thus, a new nonlinear MPC formulation is developed to navigate an AGV from its initial position to a target position at high-speed safely. First, a new cost function formulation is used that aims to find the shortest path to the target position, since no reference trajectory exists in unstructured environments. Second, a region partitioning approach is used in conjunction with a multi-phase optimal control formulation to accommodate the complicated forms the obstacle-free region can assume due to the presence of multiple obstacles in the prediction horizon in an unstructured environment. Third, the no-wheel-lift-off condition, which is the major dynamical safety concern for high-speed, high-CoG AGVs, is ensured by limiting the steering angle within a range obtained offline using a 14 degrees-of-freedom vehicle dynamics model. Thus, a safe, high-speed navigation is enabled in an unstructured environment. Simulations of an AGV approaching multiple obstacles are provided to demonstrate the effectiveness of the algorithm.

This paper presents an adaptation of the Ant System method to find the optimal control input for blood glucose regulation using Model Predictive Control (MPC). The Ant System optimization method was implemented to solve a linear MPC problem and performance was compared with the interior point method for optimization. The Ant System was found to perform well for the linear MPC problem and has the advantage over the interior point method as it can extended for use with non-linear MPC problems.

Despite recent advances in computing hardware and optimization algorithms, solving model predictive control (MPC) problems in real time still poses some technical challenges when long prediction and control horizons are used, due to the presence of several optimization variables and constraints. In this paper, we propose to reduce the computational burden by shortening the prediction and control horizon to a single step while preserving good closed-loop performance. This is achieved by using machine learning techniques to construct a tailored quadratic and convex terminal cost that approximates the cost-to-go function of constrained linear (possibly parameter-dependent) MPC formulations. The potentials of the proposed MPC with Learned Terminal Cost (LTC-MPC) approach is demonstrated in two numerical examples.

This paper presents a novel function of energy-optimal adaptive cruise control (EACC) for electric vehicles based on model predictive control (MPC), which optimally plans the host car's speed trajectory for higher energy efficiency through taking the surrounding traffic information and the road conditions ahead into account. To cope with the nonlinearity of the system dynamics, nonlinear MPC (NMPC) is designed in this paper. Afterwards, the nonlinear equality constraints are relaxed so that the optimization problem has a convex feasible set. Moreover, it is proven that the nonlinear problem can be recast as a second-order cone programming (SOCP) problem. The performance of NMPC is evaluated in the real driving condition and compared to both linear MPC and receding horizon dynamic programming (RH-DP). In order to enable real-time control, the interior point method is used to solve both linear and nonlinear MPC problems and the computation time is investigated in this paper.

In this paper, we provide a method for a quadrotor to track a ground moving target (GMT). The least squares method is used to obtain a series of reference trajectories generated by the GMT. The tracking is accomplished by applying a novel nonlinear model predictive control (MPC) scheme. The nonlinear MPC scheme applied can deal with the dynamic trajectory tracking problem of nonlinear systems by using reference generic terminal ingredients. After obtaining the reachable reference trajectories and calculating the terminal ingredients of the nonlinear MPC problem, the nonlinear MPC problem can be solved online to obtain the control inputs that enable the quadrotor to accurately track the GMT. A simulation experiment is conducted to verify the efficacy of this method.

We propose a traffic control approach that can reduce both traffic emissions and travel times based on model predictive control (MPC). We approximate the traffic flow and emission models into a linear parameter varying (LPV) form, which leads to an LPV-MPC control approach. We consider two objective functions and formulate them as convex functions, so that convex optimization methods can be used to generate the optimal control sequences of the LPV-MPC control approach. The resulting LPV-MPC solutions can next be used as a good initial point in the nonlinear-nonconvex optimization of the nonlinear original MPC problem.