Control Algorithm For Nonlinear Systems Research Articles

OCSANA+: optimal control and simulation of signaling networks from network analysis.

OCSANA+ is a Cytoscape app for identifying nodes to drive the system toward a desired long-term behavior, prioritizing combinations of interventions in large-scale complex networks, and estimating the effects of node perturbations in signaling networks, all based on the analysis of the network's structure. OCSANA+ includes an update to optimal combinations of interventions from network analysis software tool with cutting-edge and rigorously tested algorithms, together with recently developed structure-based control algorithms for non-linear systems and an algorithm for estimating signal flow. All these algorithms are based on the network's topology. OCSANA+ is implemented as a Cytoscape app to enable a user interface for running analyses and visualizing results. OCSANA+ app and its tutorial can be downloaded from the Cytoscape App Store or https://veraliconaresearchgroup.github.io/OCSANA-Plus/. The source code and computations are available in https://github.com/VeraLiconaResearchGroup/OCSANA-Plus_SourceCode. Supplementary data are available at Bioinformatics online.

Adaptive Nonlinear Control With Contraction Metrics

This letter derives direct adaptive control algorithms for nonlinear systems nominally contracting in closed-loop, but subject to structured parametric uncertainty. The approach is more general than methods based on feedback linearization or backstepping as it does not require invertibility or the system be in strict-feedback form. More broadly, it can be combined with learned controllers that must remain effective in the presence of structured parametric uncertainty. Simulation results illustrate the approach on a system with extended matched uncertainty.

Simulation software for assessment of nonlinear and adaptive multivariable control algorithms: Glucose–insulin dynamics in Type 1 diabetes

A simulator for testing automatic control algorithms for nonlinear systems with time-varying parameters, variable time delays, and uncertainties is developed. It is based on simulation of virtual patients with Type 1 diabetes (T1D). Nonlinear models are developed to describe glucose concentration (GC) variations based on user-defined scenarios for meal consumption, insulin administration, and physical activity. They compute GC values and physiological variables, such as heart rate, skin temperature, accelerometer, and energy expenditure, that are indicative of physical activities affecting GC dynamics. This is the first simulator designed for assessment of multivariable controllers that consider supplemental physiological variables in addition to GC measurements to improve glycemic control. Virtual patients are generated from distributions of identified model parameters using clinical data. The simulator will enable testing and evaluation of new control algorithms proposed for automated insulin delivery as well as various control algorithms for nonlinear systems with uncertainties, time-varying parameters and delays.

Consensus in first-order nonlinear multi-agent systems with state time delays using adaptive fuzzy wavelet networks

In this paper, a consensus problem is addressed for first-order multi-agent systems with unknown nonlinear dynamics under undirected graphs. Adaptive fuzzy wavelet networks are used to design two novel control algorithms for nonlinear systems without delays and nonlinear systems with state time delays. In these algorithms, adaptive fuzzy wavelet networks are employed to compensate for nonlinear dynamics of systems. Using proper Lyapunov functions, adaptive laws are obtained and the uniform ultimately bounded stability of closed-loop systems is proved. In addition, this paper uses Lyapunov–Krasovskii functions to handle unknown time delays. Three simulation examples are provided to illustrate the effectiveness of the proposed control schemes.

Model Predictive Control of Nonlinear Discrete Time Systems with Guaranteed Stability

AbstractThis paper presents the design of a new robust model predictive control algorithm for nonlinear systems represented by a linear model with unstructured uncertainty. The linear model is obtained by linearizing the nonlinear system at an operating point and the difference between the nonlinear and linear model is considered as a Lipschitz nonlinear function. The controller is designed for the linear model, which fulfills the stabilization condition for the nonlinear term. Unlike previous studies that have not considered a valid Lipschitz matrix of nonlinear term in the design process, we propose an algorithm in this paper in which it is considered. Therefore, the closed loop stability of the nonlinear system is guaranteed. A novel SOS optimization problem to determine design parameters is introduced, which leads to improved closed‐loop performance in comparison to a trial and error tuning procedure. Furthermore, an algorithm is presented to enlarge the region of attraction for the nonlinear closed‐loop system. Stability is improved by checking some additional conditions if which the system may be unstable if not considered. The validity of the proposed algorithm is confirmed by examples.

Adaptive TOPSIS fuzzy CMAC back-stepping control system design for nonlinear systems

This paper aims to propose a more efficient control algorithm for nonlinear systems. A novel adaptive Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) fuzzy cerebellar model articulation controller (FCMAC) back-stepping control system is developed. The proposed adaptive TOPSIS FCMAC (ATFCMAC) incorporates a multi-criteria decision analysis with a fuzzy CMAC structure to determine the optimal threshold values for selecting suitable firing nodes, improving the computational efficiency, reducing the number of firing rules, and achieving good performance for nonlinear systems. A back-stepping technique is employed for the control system design. The proposed control system comprises an ATFCMAC and a robust compensator; the ATFCMAC is used to approximate an ideal controller and the robust compensator is used to reduce the influence of residual approximation error between the ideal controller and the ATFCMAC. The parameters of the proposed ATFCMAC are tuned online using the adaptation laws that are derived from a Lyapunov stability theorem, so that the stability of the control system is guaranteed. The simulation and experimental results for a Duffing–Holmes chaotic system and a magnetic ball levitation system are used to verify the effectiveness of the proposed control scheme.

Sliding Mode Control of Constrained Nonlinear Systems

This technical note introduces the design of sliding mode control algorithms for nonlinear systems in the presence of hard inequality constraints on both control and state variables. Relying on general results on minimum-time higher-order sliding mode for unconstrained systems, a general order control law is formulated to robustly steer the state to the origin, while satisfying all the imposed constraints. Results on minimum-time convergence to the sliding manifold, as well as on the maximization of the domain of attraction, are analytically proved for the first-order and second-order sliding mode cases. A general result is presented regarding the domain of attraction in the general order case, while numerical results on the estimation of the domain of attraction and on minimum-time convergence are discussed for the third-order case, following a procedure applicable to a sliding mode of any order.

Event-triggered optimal tracking control of nonlinear systems

Summary We propose a novel event-triggered optimal tracking control algorithm for nonlinear systems with an infinite horizon discounted cost. The problem is formulated by appropriately augmenting the system and the reference dynamics and then using ideas from reinforcement learning to provide a solution. Namely, a critic network is used to estimate the optimal cost while an actor network is used to approximate the optimal event-triggered controller. Because the actor network updates only when an event occurs, we shall use a zero-order hold along with appropriate tuning laws to encounter for this behavior. Because we have dynamics that evolve in continuous and discrete time, we write the closed-loop system as an impulsive model and prove asymptotic stability of the equilibrium point and Zeno behavior exclusion. Simulation results of a helicopter, a one-link rigid robot under gravitation field, and a controlled Van-der-Pol oscillator are presented to show the efficacy of the proposed approach. Copyright © 2016 John Wiley & Sons, Ltd.

Iterated non-linear model predictive control based on tubes and contractive constraints

This paper presents a predictive control algorithm for non-linear systems based on successive linearizations of the non-linear dynamic around a given trajectory. A linear time varying model is obtained and the non-convex constrained optimization problem is transformed into a sequence of locally convex ones. The robustness of the proposed algorithm is addressed adding a convex contractive constraint. To account for linearization errors and to obtain more accurate results an inner iteration loop is added to the algorithm. A simple methodology to obtain an outer bounding-tube for state trajectories is also presented. The convergence of the iterative process and the stability of the closed-loop system are analyzed. The simulation results show the effectiveness of the proposed algorithm in controlling a quadcopter type unmanned aerial vehicle.

Formula omitted] fuzzy adaptive tracking control design for nonlinear systems with output delays

In this study, we develop fuzzy adaptive tracking control via two-layer fuzzy observers, variable structure systems (VSS), and H∞ control algorithm for nonlinear systems with plant uncertainties, output delays, and external disturbances. The Takagi–Sugeno fuzzy dynamic model with adaptation capability is used to approximate the nonlinear system. When the system states are not available, the states estimated from two-layer fuzzy observers combined with VSS are used to develop the fuzzy adaptive controller. In the first layer, the output delays are partitioned into m+1 equal time intervals to construct the same number of fuzzy observers. The output delayed states in each time interval are used as the premise variables in the IF–THEN rules. The second layer of the fuzzy observers uses output delayed error states as its linguistic variables and it is defuzzified from the first layer. Next, we develop a fuzzy adaptive controller to overcome the nonlinearities, output delayed states, and external disturbances such that H∞ tracking performance is achieved. The Lyapunov criterion and linear matrix inequalities are used to derive the controller. In the present study, our previous method is extended to handle a class of uncertain nonlinear systems with output delays and external disturbances, which is achieved using robust VSS and H∞ control techniques. A magnetic levitation system and inverted pendulum system are used as simulation examples to illustrate the validity and confirm the performance of our proposed scheme.

Sliding-mode control design for nonlinear systems using probability density function shaping.

In this paper, we propose a sliding-mode-based stochastic distribution control algorithm for nonlinear systems, where the sliding-mode controller is designed to stabilize the stochastic system and stochastic distribution control tries to shape the sliding surface as close as possible to the desired probability density function. Kullback-Leibler divergence is introduced to the stochastic distribution control, and the parameter of the stochastic distribution controller is updated at each sample interval rather than using a batch mode. It is shown that the estimated weight vector will converge to its ideal value and the system will be asymptotically stable under the rank-condition, which is much weaker than the persistent excitation condition. The effectiveness of the proposed algorithm is illustrated by simulation.

Neural-Genetic Control Algorithm of Nonlinear Systems

Control of nonlinear systems is a challenging task. One of the ways of control of such systems is the use of neural networks as controllers. In this paper a methodology is proposed, where for neural controller design the genetic algorithm has been used. This method allows find optimal adjustment of neural network weights so that high performance is obtained. The proposed control method is realized in Matlab/Simulink and demonstrated on two examples of nonlinear dynamical systems.

Convergence monotonicity and speed comparison of iterative learning control algorithms for nonlinear systems

Convergence monotonicity and speed comparison of iterative learning control algorithms for nonlinear systems

A back propagation through time-like min-max optimal control algorithm for nonlinear systems

This paper presents a conjugate gradient-based algorithm for feedback min–max optimal control of nonlinear systems. The algorithm has a backward- in-time recurrent structure similar to the back propagation through time (BPTT) algorithm. The control law is given as the output of the one- layer NN. Main contribution of the paper includes the integration of BPTT techniques, conjugate gradient methods, Adams method for solving ODEs and automatic differentiation, to provide an effective, numerically robust algorithm for solving optimal min–max control problems. The proposed algorithm is evaluated on a robotic system with two DOFs.

Indirect Adaptive Fuzzy Control for a Class of Uncertain Nonlinear Systems with Unknown Control Direction

In this paper, the authors propose two indirect adaptive fuzzy control schemes for a class of uncertain continuous-time single-input single-output (SISO) nonlinear dynamic systems with known and unknown control direction. Within these schemes, fuzzy systems are used to approximate unknown nonlinear functions and the Nussbaum gain technique is used to deal with the unknown control direction. This paper first presents a singularity-free indirect adaptive control algorithm for nonlinear systems with known control direction, and then this control algorithm is generalized for the case of unknown control direction. The proposed adaptive controllers are free from singularity, allow initialization to zero of all adjustable parameters of the used fuzzy systems, and guarantee asymptotic convergence of the tracking error to zero. Simulations performed on a nonlinear system are given to show the feasibility of the proposed adaptive control schemes.

Direct neural network-based self-tuning control for a class of nonlinear systems

Most self-tuning control algorithms for nonlinear systems become invalid when the controlled systems have nonminimum phase property. In this article, a direct neural network-based self-tuning control strategy is developed to deal with this problem under the certainty equivalence principle. Based on an equivalent linearized model from the local linearization, the controller structure is designed using a modified Clarke index with the guaranteed closed-loop stability and without the traditional requirement of the globally boundedness. For the system with unknown parameters, the controller is self-tuned by an on line RBF neural network identifier. Satisfactory simulations illustrate the effectiveness and adaptability of the proposed strategy even under system parameter variations.

A scheduling quasi–min-max model predictive control algorithm for nonlinear systems

Abstract In this paper, a model predictive control algorithm is designed for nonlinear systems. Combination of a linear model with a linear parameter varying model approximates the nonlinear behavior. The linear model is used to express the current nonlinear dynamics, and the linear parameter varying model is used to cover the future nonlinear behavior. In the algorithm, a “quasi-worst-case” value of an infinite horizon objective function is minimized. Closed-loop stability is guaranteed when the algorithm is implemented in a receding horizon fashion by including a Lyapunov constraint in the formulation. The proposed approach is applied to control a jacketed styrene polymerization reactor.

A stabilizing model-based predictive control algorithm for nonlinear systems

Predictive control of nonlinear systems subject to state and input constraints is considered. Given an auxiliary linear control law, a good nonlinear receding-horizon controller should (i) be computationally feasible, (ii) enlarge the stability region of the auxiliary controller, and (iii) approximate the optimal nonlinear infinite-horizon controller in a neighbourhood of the equilibrium. The proposed scheme achieves these objectives by using a prediction horizon longer than the control one in the finite-horizon cost function. This means that optimization is carried out only with respect to the first few input moves whereas the state movement is predicted (and penalized) over a longer horizon where the remaining input moves are computed using the auxiliary linear control law. Closed-loop stability is ensured by means of a penalty on the terminal state which is a computable approximation of the infinite-horizon cost associated with the auxiliary controller. As an illustrative example, the predictive control of a highly nonlinear chemical reactor is discussed.

Nonlinear Model Predictive Control: Control and Prediction Horizon

In this paper a new class of Model Predictive control algorithms for nonlinear systems is introduced. A prediction horizon longer than the control horizon is used. It is shown that in this way it is possible to enlarge the domain of attraction and to improve the performance without enlarging the dimension of the optimization space. The idea is developed to solve the regulation problem and the tracking problem for reference signals constant beyond a prescribed future horizon.

Adaptive Decentralized Control for a Class of Nonlinear Systems

The problems of nonlinear complex system control design are still in the centre of attention and there exists no universal solution by now. The aim of this paper is to propose the control algorithm for nonlinear systems consisting of several subsystems. The subsystem nonlinearities are assumed to be known and the state variables are accessible only locally. The interactions between subsystems can be unknown, but bounded. The proposed control algorithm for such class of complex systems is based on the feedback linearization technique with automatic adjusting of the subsystem decay rate. The control performances are illustrated by an example of nonlinear system consisting of two interconnected subsystems.