Nonlinear Constrained Model Research Articles

Optimal path planning of Unmanned Aerial Vehicles (UAVs) for targets touring: Geometric and arc parameterization approaches.

The path planning problem for unmanned aerial vehicles (UAVs) is important for scheduling the UAV missions. This paper presents an optimal path planning model for UAV to control its direction during target touring, where UAV and target are at the same altitude. Geometric interpretation of the given model is provided when the vehicles consider connecting an initial position to the destination position with specific target touring. We develop a nonlinear constrained model based on an arc parameterization approach to determine the UAV's optimal path touring a target. The model is then extended to touring finite numbers of targets and optimizing the routes. The model is found reliable through several simulations. Numerical experiments are conducted and we have shown that the UAV's generated path satisfies vehicle dynamics constraints, tours the targets, and arrives at its destination.

A variational non-linear constrained model for the inversion of FDEM data* *Dedicated to Lothar Reichel on the occasion of his 70th birthday.

Reconstructing the structure of the soil using non-invasive techniques is a very relevant problem in many scientific fields, like geophysics and archaeology. This can be done, for instance, with the aid of frequency domain electromagnetic (FDEM) induction devices. Inverting FDEM data is a very challenging inverse problem, as the problem is extremely ill-posed, i.e. sensible to the presence of noise in the measured data, and non-linear. Regularization methods substitute the original ill-posed problem with a well-posed one whose solution is an accurate approximation of the desired one. In this paper we develop a regularization method to invert FDEM data. We propose to determine the electrical conductivity of the ground by solving a variational problem. The minimized functional is made up by the sum of two term: the data fitting term ensures that the recovered solution fits the measured data, while the regularization term enforces sparsity on the Laplacian of the solution. The trade-off between the two terms is determined by the regularization parameter. This is achieved by minimizing an ℓ 2 − ℓ q functional with 0 < q ⩽ 2. Since the functional we wish to minimize is non-convex, we show that the variational problem admits a solution. Moreover, we prove that, if the regularization parameter is tuned accordingly to the amount of noise present in the data, this model induces a regularization method. Some selected numerical examples on synthetic and real data show the good performances of our proposal.

Forward-looking persistent excitation in model predictive control

This work deals with the problem of integrating persistence of excitation into nonlinear constrained model predictive control to estimate uncertain parameters while guaranteeing a stable closed loop. We propose an adaptive tracking model predictive control and conditions which guarantee persistent excitation and uniformly bounded closed loop signals of nonlinear systems, despite bounded noise and parameter uncertainty. This is achieved by actively designing persistence of excitation through the computation of a reference trajectory around some nominal stationary point depending on the parameter estimate, opening up the opportunity of balancing excitation against other requirements. Appealing to the Total Stability Theorem, the results are local and solution evolves in a non-infinitesimal ball in state and estimated parameter.

Constrained nonlinear model predictive control of pH value in wet flue gas desulfurization process

AbstractIn wet flue gas desulfurization (WFGD) process, the pH value of the absorption tower slurry is a crucial factor to the efficiency of desulfurization system. Aiming at the nonlinearity and large lag of the pH change in WFGD process, a predictive control strategy based on Hammerstein–Wiener inverse model compensation is proposed. During the calculation of optimal control, an anti‐model of Wiener nonlinearity unit is adopted to transform the output setting values and sampling values. Similarly in the control process, the controller output is applied to the actual controlled object after inverse transformation of the static nonlinear Hammerstein model. Through the above two inverse transformations, the controller output is identical with the input of linear link in the closed‐loop system. In this article, the inverse model compensation method is utilized to transform nonlinear process control into linear system control, avoiding the large computation of nonlinear model optimization. Finally, the feasibility and effectiveness of the proposed scheme are verified by simulation.

A Constrained Non-Linear Model Predictive Controller for the Rotor Flux-Oriented Control of an Induction Motor Drive

Predictive controllers have been extensively studied and applied to electrical drives, mainly because they provide fast dynamic responses and are suitable for multi-variable control and non-linear systems. Many approaches perform the prediction and optimization process on-line, which requires a high computational capacity for fast dynamics, such as, for example, the control of AC electric motors. Due to the complexity of embedding constraints in controller design, which demands a high computational capacity to solve the optimization problem, off-line approaches are one of the choices to overcome this problem. However, these strategies do not deal with the inherent constraints of the drive system, which significantly simplifies the design of the controller. This paper proposes a non-linear and multi-variable predictive controller to control the speed and rotor flux of an induction motor, where the constraints are treated after the controller design. Besides dealing with the constraints of the electric drive system, our proposal allows increasing the stability of the system when the model does not incorporate disturbances and when parameter incompatibilities occur. Several computer simulations and experimental tests were performed to evaluate the behavior of the proposed controller, showing good performance to track the controlled variables under normal operating conditions, under load disturbances, parametric incompatibility, and at a very low rotor speed.

Design and Implementation of Observer-Based Sliding Mode for Underactuated Rendezvous System

This article addresses the design and implementation of observer-based sliding mode controller with H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> performance for underactuated rendezvous system under the constraints of fault signals, maximum input, and disturbances. The nonlinear constrained model considered in this article is an underactuated system since the number of control input variables is less than that of state variables, besides, owing to the full state information is unavailable or not so accurate for the controller design, an observer is first constructed to estimate the full state of system, and then the state of observer is adopted to synthesize the integral-type sliding surface function. Considering three fault signals, input constraint, and disturbances, the stability criteria with H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> performance are derived based on Lyapunov method and the ellipsoidal approximation algorithm. Furthermore, the sliding mode control law is formulated to guarantee the sliding mode dynamic could be driven onto the sliding surface and remain there for subsequent time. Finally, the simulation experiments are implemented to verify the effectiveness of the proposed scheme for the underactuated rendezvous system.

Constrained nonlinear model predictive control for centrifugal compressor system surge including piping acoustic using closed coupled valve

ABSTRACTThis paper deals with nonlinear model predictive control scheme for surge prevention in centrifugal compressors systems. To bring up the effects of the station’s piping system on the compressor surge, nonlinear dynamic of compression system is considered that involve acoustic of compressor system. Close-coupled-valve (CCV), as a common control input in compression systems, is considered as an actuator and the mathematical model describing the flow dynamic of compression system is derived in the presence of CCV. For controlling the compressor system surge instability, nonlinear model predictive control (NMPC) is applied, whose allow to consider constraints on CCV actuator and states of system, significantly enlarge the operating region of the compressor and enhance the authority of the control system. Numerical simulations show that the proposed control system is able to meet the desired specifications in avoiding and active control of surge, in the presence of different types of disturbances occurring along the pipeline.

A Perturbed Chord (Newton-Kantorovich) Method for Constrained Nonlinear Model Predictive Control

Abstract: An approach to the computational implementation of Constrained Nonlinear Model Predictive Control (CNMPC) algorithms is described based on exploiting the modified Newton’s method originally proposed by Kantorovich for solving nonlinear equations. This method is distinguished by avoiding the need to compute the Jacobian at each iteration while still ensuring convergence. In this paper, new results characterizing the convergence of this method while accounting for perturbations that may result from various approximations are obtained. Examples illustrating the potential of the proposed approach for spacecraft attitude control and diesel engine air path control are reported. They indicate that good tracking performance can be achieved and constraints can be enforced while the computational effort is reduced.

Generalized Stabilizing Conditions for Model Predictive Control

This note addresses the tracking problem for model predictive control. It presents simple procedures for both linear and nonlinear constrained model predictive control when the desired equilibrium state is any point in a specified set. The resultant region of attraction is the union of the regions of attraction for each equilibrium state in the specified set and is therefore larger than that obtained when conventional model predictive control is employed.

Layout of flexible manufacturing systems based on kinematic constraints of the autonomous material handling system

This paper presents a research that investigates solutions and algorithms for determining the optimum machine layout served by autonomous material handling system, like mobile robot or automated guided vehicle. Unlike previous works which solved the layout problem by optimizing the distance between facilities, in this paper the machine layout is addressed based on optimizing the travel time of the material handling system. The proposed approach can include boundary kinematic constraints of vehicle while optimizing the objective function such as velocity, acceleration, orientation, and trajectory curvature. The nonlinear constrained model is transformed to unconstrained problem using penalty method. Then, a simulated annealing-based algorithm is used to search for the optimum locations of machines among all possible feasible layouts. The simulation results showed that the proposed approach was efficient enough to use in real factories due to including a vehicle path planner integrated in an overall layout design scheme that involves searching of vehicle control parameters.

Constrained Nonlinear Model Predictive Control of a Polymerization Process via Evolutionary Optimization

In this work, a nonlinear model predictive controller is developed for a batch polymerization process. The physical model of the process is parameterized along a desired trajectory resulting in a trajectory linearized piecewise model (a multiple linear model bank) and the parameters are identified for an experimental polymerization reactor. Then, a multiple model adaptive predictive controller is designed for thermal trajectory tracking of the MMA polymerization. The input control signal to the process is constrained by the maximum thermal power provided by the heaters. The constrained optimization in the model predictive controller is solved via genetic algorithms to minimize a DMC cost function in each sampling interval.

Derivative-free Estimator Based Non-Linear Model Predictive Control of a Boiler-Turbine Unit

In this work, the authors have proposed a constrained nonlinear model predictive control (NMPC) scheme for a boiler-turbine system. The proposed control scheme relies on the non-linear state space model proposed by Bell and Astrom, 1987 for prediction. A derivative-free Kalman filter has been designed to estimate the state variables of the boiler-turbine unit. These estimated values have been used as an initial condition for predicting the future states and outputs in the NMPC formulation. In order to account for model-plant mismatch and to achieve offset-free control, innovation based correction of predicted states and outputs as suggested by Ricker, 1990 has been incorporated in the proposed NMPC formulation. The extensive simulation studies show that the proposed control scheme effectively handles the input constraints of the boiler-turbine unit and meets the required electrical demand without requiring careful selection of operating points.

Convergence Guaranteed Nonlinear Constraint Model Predictive Control via I/O Linearization

Constituting reliable optimal solution is a key issue for the nonlinear constrained model predictive control. Input-output feedback linearization is a popular method in nonlinear control. By using an input-output feedback linearizing controller, the original linear input constraints will change to nonlinear constraints and sometimes the constraints are state dependent. This paper presents an iterative quadratic program (IQP) routine on the continuous-time system. To guarantee its convergence, another iterative approach is incorporated. The proposed algorithm can reach a feasible solution over the entire prediction horizon. Simulation results on both a numerical example and the continuous stirred tank reactors (CSTR) demonstrate the effectiveness of the proposed method.

Stability Analysis of Constrained Nonlinear Model Predictive Control with Terminal Weighting

This paper investigates stability of model predictive control (MPC) for nonlinear constrained systems. New stability results for the MPC algorithms with terminal weighting are proposed using the dynamic programming method, which gives new criteria for choosing state, control and terminal weighting in the performance index to achieve stability of MPC algorithms. Illustrative examples are given to show that by combining this condition with existing ones, much less conservative results can be generated.

On all-propulsion design of integrated orbit and attitude control for inner-formation gravity field measurement satellite

The inner-formation gravity field measurement satellite (IFS) is a novel pure gravitational orbiter. It aims to measure the Earth’s gravity field with unprecedented accuracy and spatial resolution by means of precise orbit determination (POD) and relative state measurement. One of the key factors determining the measurement level is the outer-satellite control used for keeping the inner-satellite flying in a pure gravitational orbit stably. In this paper the integrated orbit and attitude control of IFS during steady-state phase was investigated using only thrusters. A six degree-of-freedom translational and rotational dynamics model was constructed considering nonlinearity resulted from quaternion expression and coupling induced by community thrusters. A feasible quadratic optimization model was established for the integrated orbit and attitude control using constrained nonlinear model predictive control (CNMPC) techniques. Simulation experiment demonstrated that the presented CNMPC algorithm can achieve rapid calculation and overcome the non-convexity of partial constraints. The thruster layout is rational with low thrust consumption, and the mission requirements of IFS are fully satisfied.

Mixed immunotherapy and chemotherapy of tumors: Feedback design and model updating schemes

In this paper, a recently developed model governing the cancer growth on a cell population level with combination of immune and chemotherapy is used to develop a reactive (feedback) mixed treatment strategy. The feedback design proposed here is based on nonlinear constrained model predictive control together with an adaptation scheme that enables the effects of unavoidable modeling uncertainties to be compensated. The effectiveness of the proposed strategy is shown under realistic human data showing the advantage of treatment in feedback form as well as the relevance of the adaptation strategy in handling uncertainties and modeling errors. A new treatment strategy defined by an original optimal control problem formulation is also proposed. This new formulation shows particularly interesting possibilities since it may lead to tumor regression under better health indicator profile.

A tool to analyze robust stability for constrained nonlinear MPC

A sufficient condition for robust asymptotic stability of nonlinear constrained model predictive control (MPC) is derived with respect to plant/model mismatch. This work is an extension of a previous study on the unconstrained nonlinear MPC problem, and is based on nonlinear programming sensitivity concepts. It addresses the discrete time state feedback problem with all states measured. A strategy to estimate bounds on the plant/model mismatch is proposed that can be used off-line as a tool to assess the extent of model mismatch that can be tolerated to guarantee robust stability.

Constrained quadratic stabilization of discrete-time uncertain nonlinear multi-model systems using piecewise affine state-feedback

In this paper a method for nonlinear robust stabilization based on solving a bilinear matrix inequality (BMI) feasibility problem is developed. Robustness against model uncertainty is handled. In different non-overlapping regions of the state-space called clusters the plant is assumed to be an element in a polytope which vertices (local models) are affine systems. In the clusters containing the origin in their closure, the local models are restricted to be linear systems. The clusters cover the region of interest in the state-space. An affine state-feedback is associated with each cluster. By utilizing the affinity of the local models and the state-feedback, a set of linear matrix inequalities (LMIs) combined with a single nonconvex BMI are obtained which, if feasible, guarantee quadratic stability of the origin of the closed-loop. The feasibility problem is attacked by a branch-and-bound based global approach. If the feasibility check is successful, the Liapunov matrix and the piecewise affine state-feedback are given directly by the feasible solution. Control constraints are shown to be representable by LMIs or BMIs, and an application of the control design method to robustify constrained nonlinear model predictive control is presented. Also, the control design method is applied to a simple example.