Multiple-input Multiple-output Nonlinear Systems Research Articles

Global adaptive neural tracking control of nonlinear MIMO systems

This paper addresses the globally stable tracking control problem of a class of uncertain multiple-input–multiple-output nonlinear systems. By employing the radial basis function neural networks to compensate for the system uncertainties, a novel switching controller is developed. The key features of the proposed control scheme are presented as follows. First, to design the desired adaptive neural controller successfully, an nth-order smoothly switching function is constructed originally. Second, the number of the neural networks and the adaptive parameters is reduced by adopting the direct adaptive approach, so a simplified controller is designed and it is easy to implement in practice. By utilizing the special properties of the affine terms of the considered systems, the singularity problem of the controller is completely avoided. Finally, the overall controller guarantees that all the signals in the closed-loop system are globally uniformly ultimately bounded and the system output converges to a small neighborhood of the reference trajectory by appropriately choosing the design parameters. A simulation example is given to illustrate the effectiveness of the proposed control scheme.

Adaptive Neural Control of Uncertain MIMO Nonlinear Systems With State and Input Constraints.

An adaptive neural control strategy for multiple input multiple output nonlinear systems with various constraints is presented in this paper. To deal with the nonsymmetric input nonlinearity and the constrained states, the proposed adaptive neural control is combined with the backstepping method, radial basis function neural network, barrier Lyapunov function (BLF), and disturbance observer. By ensuring the boundedness of the BLF of the closed-loop system, it is demonstrated that the output tracking is achieved with all states remaining in the constraint sets and the general assumption on nonsingularity of unknown control coefficient matrices has been eliminated. The constructed adaptive neural control has been rigorously proved that it can guarantee the semiglobally uniformly ultimate boundedness of all signals in the closed-loop system. Finally, the simulation studies on a 2-DOF robotic manipulator system indicate that the designed adaptive control is effective.

Adaptive sensor-fault tolerant control for a class of MIMO uncertain nonlinear systems: Adaptive nonlinear filter-based dynamic surface control

This paper presents an adaptive fault tolerant control (FTC) scheme for a class of multiple-input multiple-output (MIMO) nonlinear systems against sensor faults, modeling errors and external disturbances. Four kinds of sensor faults including bias, drift, loss of accuracy and loss of effectiveness can be tolerated by the proposed FTC system. Within this scheme, dynamic surface control (DSC) technique, robust adaptation laws and adaptive nonlinear filters are combined for designing an adaptive dynamic surface control (ADSC)-based FTC system in order to compensate for the effects of sensor faults and system uncertainties (including external disturbances, modeling errors and unexpected nonlinear functions caused by sensor faults). Lyapunov approach is used to prove that all the signals in the closed-loop system are bounded and the tracking-errors can be forced to converge into a small neighborhood of zero. The feasibility and the effectiveness of the proposed FTC controller are demonstrated through two simulation examples.

Teaching Aids for Laboratory Experiments with AR.Drone2 Quadrotor

The goal of the paper is to create low-cost quadrotor laboratory experiments for undergraduate and graduate students at automation departments. We present tutorials for various experiments with the AR.Drone2 quadrotor. This device is an eye-catching and versatile system where students can solve problems in various areas of modeling, identification, and control of multiple-input multiple-output (MIMO) nonlinear systems. A software interface for experiments is based on Robot Operating System (ROS) and Ardrone_autonomy package. It is possible to use different programming languages like C++, Python and Lisp within the ROS depending on a user’s preference. In the paper we present basic characteristics of the AR.Drone2, a suitable modeling approach, system identification from input-output data, state observation, and control design. We accentuate an experimental validation.

Nonlinear model predictive control based on support vector machine and genetic algorithm

This paper presents a nonlinear model predictive control (NMPC) approach based on support vector machine (SVM) and genetic algorithm (GA) for multiple-input multiple-output (MIMO) nonlinear systems. Individual SVM is used to approximate each output of the controlled plant. Then the model is used in MPC control scheme to predict the outputs of the controlled plant. The optimal control sequence is calculated using GA with elite preserve strategy. Simulation results of a typical MIMO nonlinear system show that this method has a good ability of set points tracking and disturbance rejection.

Tracking Controller Design for MIMO Nonlinear Systems With Application to Automotive Cold Start Emission Reduction

The main contribution of this paper is the development of a nonlinear multiple-input, multiple-output (MIMO) tracking controller design using a discrete time sliding control approach. A Lyapunov stability analysis is used to prove the asymptotic stability of both the output errors as well as the parameter estimation errors. The application of the “New Invariance Principle” is key to the proof of the parameter error convergence. The developed approach is applied to the cold start emissions problem. The software design process for automotive powertrains on vehicles is growing increasingly complex. Verification and validation provides a systematic procedure to follow for the implementation of control algorithms on physical systems. However, errors can arise that prove costly if not mitigated early on in the verification and validation process. Therefore, the detection and mitigation of potential uncertainties early on in the design process is vital. In this work, the determination of the system model uncertainty is the focus of an adaptation algorithm designed in parallel with a discrete time, MIMO sliding controller. The unknown parameter representing the model uncertainty is updated online in order to decrease tracking error and control effort. The MIMO formulation allows for implementation of both coupled and decoupled frameworks, thus providing a basis for the algorithm to be utilized on a variety of complex vehicle systems. The control algorithms are implemented on a cold start emissions engine model as a case study. A matlab simulink environment is used for simulation results, and an engine test cell is used for experimental validation. Simulation results demonstrate that the algorithm drives tracking error to zero in a fraction of the run time and that the algorithm may be applied with equal efficacy to coupled and decoupled systems. Experimental results demonstrate the ability of the adaptation algorithm to estimate uncertainty in the engine and decrease tracking error.

Multiple-Input Multiple-Output Optical Integrator Design by Non-Interacting Control via Dynamic Extension

Semiconductor optical amplifiers (SOAs) have recently attracted much attention as the potential building blocks for active photonic circuits. They are being used in many applications of optical signal processing in addition to amplification of the optical signal. Their use as wavelength converters and optical logic gates has been demonstrated [1,2]. In this paper we propose an SOA based design of a multiple-input multiple-output integrator for optical signals. The design is based on non-interacting state feedback control through dynamic extension. If a nonlinear dynamical system takes the form of Equation (1) where, z is in Rn , f, g and h are n-dimensional smooth vector fields in the neighborhood of z0 in Rn , and it also has a well-defined vector relative degree in the neighborhood of z0, it is well known in the nonlinear control literature that the system can be transformed into a chain of integrators by state feedback [3]. Moreover, the effect of such feedback will result in the outputs which are completely decoupled from each other, with each output yi being affected only by the corresponding input, ui, hence it is named non-interacting control. This control method is commonly used in nonlinear multiple-input multiple-output systems. From the physical governing equations of SOA, the state space model for the device was developed by Knutze et. al, in [4] in the form of Equation (2), where z is the charge carrier density and RA, RB and RC are, respectively, linear, bimolecular and Auger recombination coefficients; I is the electric current, q is the charge of an electron; and V and L are, respectively, the volume and the length of SOA. For each optical channel: ui is the input and, Gi(x)=aiγi(z-ztr,i) is the gain function; ai is the differential gain, γi is the confinement factor; ztr,i is the transparency carrier density; ωc,i is the carrier frequency; and αi is the waveguide loss. The signals yi are the optical outputs. Equation (2) does not take the form of (1) because it has the inputs directly appearing in the outputs. Thus, non-interacting control method cannot be applied directly. Therefore, the dynamics of the system are extended by renaming z, u1 and u2 as z1, z2 and z3, respectively, and the external inputs: v1 and v2are used to control the dynamics of these extended states. Now the state space model becomes Equation (3). Since Equation (3) takes the form of Equation (1), and it was verified that the system has a well-defined vector relative degree 1 in a large range of operating points, the non-interacting feedback laws are derived and the state feedback is applied. After applying feedback, the closed loop device is simulated in Matlab Simulink and it was observed that each optical input signal ui(t) is integrated and its integral yi(t) appears at the output without inter-modal modulation. Simulation results for a pair of typical inputs are shown in Figure 1.

Neural Controller Design-Based Adaptive Control for Nonlinear MIMO Systems With Unknown Hysteresis Inputs.

This paper studies an adaptive neural control for nonlinear multiple-input multiple-output systems in interconnected form. The studied systems are composed of N subsystems in pure feedback structure and the interconnection terms are contained in every equation of each subsystem. Moreover, the studied systems consider the effects of Prandtl-Ishlinskii (PI) hysteresis model. It is for the first time to study the control problem for such a class of systems. In addition, the proposed scheme removes an important assumption imposed on the previous works that the bounds of the parameters in PI hysteresis are known. The radial basis functions neural networks are employed to approximate unknown functions. The adaptation laws and the controllers are designed by employing the backstepping technique. The closed-loop system can be proven to be stable by using Lyapunov theorem. A simulation example is studied to validate the effectiveness of the scheme.

Decoupling control for two-axis inertially stabilized platform based on an inverse system and internal model control

This paper describes a decoupling control scheme for a two-axis inertially stabilized platform (ISP) used in the airborne power line inspection system. The dynamic model of the ISP has been obtained by using the Newton–Euler equation first. The inverse system method combining with the internal model control has been proposed to deal with the nonlinearity and coupling of the ISP. The key idea is to design an inverse system with measured system states such as angular positions, rates and accelerations. Then a pseudo-linear system is constructed when the inverse system is connected with the original system in series. As a result, the coupled nonlinear MIMO (Multiple-Input Multiple-Output) system is converted to two linear decoupled SISO (Single-Input Single-Output) subsystems. Model uncertainties or unmeasurable disturbances existing objectively can be solved by introducing internal model control. Better decoupling effect and disturbance rejecting ability are demonstrated by numerical simulations and experiments carried out on a two-axis ISP system.

Robust Control Applied to Multiple-Input Multiple-Output Nonlinear Systems

Many of practical systems (for example: robotic systems, power systems and electronic circuits) are multiple-input multiple-output nonlinear systems and some of them have coupling between inputs and outputs. Besides all that, these systems can suffer with parametric uncertainties and external disturbances. Any control techniques applied to these systems are complex. This work presents a control structure, based on the union between a modified version of the variable structure model reference adaptive control and a left-inverse decoupling technique, to transform a multiple-input multiple output nonlinear system into a set of single-input single-output linear systems. In that case each input affects only one output and with a desired closed-loop performance. The proposed structure transforms the variable structure model reference adaptive control, which is usually applied to single-input single-output linear systems, into a controller to be applied to a class of multiple-input multiple-output nonlinear systems. It is important to note that proposed structure, using only input/output measurements, presents fast transient performance, reduces the output “chattering” and it is robust to parametric uncertainties and disturbances. All these features are verified by simulation results of an electronic circuit that exhibits chaotic behavior (Chua’s circuit).

On the ℓ2-stability of time-varying linear and nonlinear discrete-time MIMO systems

New conditions are derived for the l2-stability of time-varying linear and nonlinear discrete-time multiple-input multiple-output (MIMO) systems, having a linear time time-invariant block with the transfer function Γ(z), in negative feedback with a matrix of periodic/aperiodic gains A(k), k = 0, 1, 2, … and a vector of certain classes of non-monotone/monotone nonlinearities φ(·), without restrictions on their slopes and also not requiring path-independence of their line integrals. The stability conditions, which are derived in the frequency domain, have the following features: i) They involve the positive definiteness of the real part (as evaluated on |z| = 1) of the product of Γ(z) and a matrix multiplier function of z. ii) For periodic A(k), one class of multiplier functions can be chosen so as to impose no constraint on the rate of variations A(k), but for aperiodic A(k), which allows a more general multiplier function, constraints are imposed on certain global averages of the generalized eigenvalues of (A(k + 1), A(k)), k = 1, 2, …. iii) They are distinct from and less restrictive than recent results in the literature.

Adaptive NN controller design for a class of nonlinear MIMO discrete-time systems.

An adaptive neural network tracking control is studied for a class of multiple-input multiple-output (MIMO) nonlinear systems. The studied systems are in discrete-time form and the discretized dead-zone inputs are considered. In addition, the studied MIMO systems are composed of N subsystems, and each subsystem contains unknown functions and external disturbance. Due to the complicated framework of the discrete-time systems, the existence of the dead zone and the noncausal problem in discrete-time, it brings about difficulties for controlling such a class of systems. To overcome the noncausal problem, by defining the coordinate transformations, the studied systems are transformed into a special form, which is suitable for the backstepping design. The radial basis functions NNs are utilized to approximate the unknown functions of the systems. The adaptation laws and the controllers are designed based on the transformed systems. By using the Lyapunov method, it is proved that the closed-loop system is stable in the sense that the semiglobally uniformly ultimately bounded of all the signals and the tracking errors converge to a bounded compact set. The simulation examples and the comparisons with previous approaches are provided to illustrate the effectiveness of the proposed control algorithm.

Adaptive neural control of nonlinear MIMO systems with time-varying output constraints.

In this paper, adaptive neural control is investigated for a class of unknown multiple-input multiple-output nonlinear systems with time-varying asymmetric output constraints. To ensure constraint satisfaction, we employ a system transformation technique to transform the original constrained (in the sense of the output restrictions) system into an equivalent unconstrained one, whose stability is sufficient to solve the output constraint problem. It is shown that output tracking is achieved without violation of the output constraint. More specifically, we can shape the system performance arbitrarily on transient and steady-state stages with the output evolving in predefined time-varying boundaries all the time. A single neural network, whose weights are tuned online, is used in our design to approximate the unknown functions in the system dynamics, while the singularity problem of the control coefficient matrix is avoided without assumption on the prior knowledge of control input's bound. All the signals in the closed-loop system are proved to be semiglobally uniformly ultimately bounded via Lyapunov synthesis. Finally, the merits of the proposed controller are verified in the simulation environment.

Robust decentralized hybrid adaptive output feedback fuzzy control for a class of large-scale MIMO nonlinear systems and its application to AHS

This paper presents a novel observer-based decentralized hybrid adaptive fuzzy control scheme for a class of large-scale continuous-time multiple-input multiple-output (MIMO) uncertain nonlinear systems whose state variables are unmeasurable. The scheme integrates fuzzy logic systems, state observers, and strictly positive real conditions to deal with three issues in the control of a large-scale MIMO uncertain nonlinear system: algorithm design, controller singularity, and transient response. Then, the design of the hybrid adaptive fuzzy controller is extended to address a general large-scale uncertain nonlinear system. It is shown that the resultant closed-loop large-scale system keeps asymptotically stable and the tracking error converges to zero. The better characteristics of our scheme are demonstrated by simulations.

Decentralized adaptive fuzzy control for a class of large-scale MIMO nonlinear systems with strong interconnection and its application to automated highway systems

In the previous work of Huang et al., a decentralized adaptive fuzzy controller of large-scale multiple-input multiple-output nonlinear systems is obtained predicated upon the assumption that the interconnections between subsystems can be bounded by first-order polynomials. In this note, we focus in the absence of the conservative assumption upon developing a novel decentralized adaptive fuzzy control scheme. In virtue of fuzzy systems and a regularized inverse matrix, the developed control scheme not only addresses controller singularity under an overall design framework but also copes with interconnections with arbitrary nonlinear bounds. The resulting closed-loop large-scale system is proved to be asymptotically stable. The controller design is applicable to an automated highway system, and simulation results confirm its practical usefulness.

Direct adaptive control for a class of MIMO nonlinear discrete-time systems

This paper considers the problem of adaptive control for a class of multiple input multiple output(MIMO) nonlinear discretetime systems based on inputoutput model with unknown interconnections between subsystems. Based on the Taylor expand technology, an equivalent model in affinelike form is derived for the original nonaffine nonlinear system. Then a direct adaptive neural network(NN) controller is implemented based on the affinelike model. By finding an orthogonal matrix to tune the NN weights, the closedloop system is proven to be semiglobally uniformly ultimately bounded. The σmodification technique is used to remove the requirement of persistence excitation during the adaptation. The control performance of the closedloop system is guaranteed by suitably choosing the design parameters.

Online constrained optimization based adaptive robust control of a class of MIMO nonlinear systems with matched uncertainties and input/state constraints

A performance oriented two-loop control approach is proposed for a class of multiple-input–multiple-output (MIMO) systems with input saturation, state constraints, matched parametric uncertainties and input disturbances. In the inner loop, a constrained adaptive robust control (ARC) law is synthesized to achieve the required robust tracking performances with respect to on-line replanned trajectory in the presence of input saturation and various types of matched uncertainties. In the outer loop, a replanned trajectory is generated by solving a constrained optimization algorithm online to minimize the converging time of the overall system response to the desired trajectory while not violating various constraints. Interaction of the two loops is explicitly characterized by a set of inequalities that the design variables of each loop have to satisfy. It is theoretically shown that the resulting closed-loop system can track feasible desired trajectories with a guaranteed converging time and steady-state tracking accuracy without violating the state constraints. Since the system in study is most appropriate to describe the dynamics of the robotic systems, the control of a two-axis planar robotic manipulator is used as an application example. Comparative simulation results demonstrate the advantage of the proposed approach over the traditional approaches in practical applications.

Zero Dynamics Analysis for Inverse Decoupling Control of Asynchronous Traction Motor

Considering the problem for inverse system method in EMU AC induction traction motor linear decoupling, the zero dynamics subsystem will be separated from the original dynamic system through coordinate transformation. Firstly, a getting method for zero dynamics of the multiple input multiple output nonlinear system is discussed when γ＜ n. Second, the zero dynamics analysis for five order nonlinear model of asynchronous traction motor which base on the stationary coordinate system is given by using inverse decoupling method. The analysis results show that if the stability of the zero dynamics can be ensured, then the entire linearization of original nonlinear system is not necessary, need only partial linearization which effect on the external dynamic portion. The inverse decoupling process of asynchronous traction motor can be simplified by this conclusion. DOI : http://dx.doi.org/10.11591/telkomnika.v12i1.3354

Neural network L1 adaptive control of MIMO systems with nonlinear uncertainty.

An indirect adaptive controller is developed for a class of multiple-input multiple-output (MIMO) nonlinear systems with unknown uncertainties. This control system is comprised of an L 1 adaptive controller and an auxiliary neural network (NN) compensation controller. The L 1 adaptive controller has guaranteed transient response in addition to stable tracking. In this architecture, a low-pass filter is adopted to guarantee fast adaptive rate without generating high-frequency oscillations in control signals. The auxiliary compensation controller is designed to approximate the unknown nonlinear functions by MIMO RBF neural networks to suppress the influence of uncertainties. NN weights are tuned on-line with no prior training and the project operator ensures the weights bounded. The global stability of the closed-system is derived based on the Lyapunov function. Numerical simulations of an MIMO system coupled with nonlinear uncertainties are used to illustrate the practical potential of our theoretical results.

Controller Tuning by Means of Multi-Objective Optimization Algorithms: A Global Tuning Framework

A holistic multi-objective optimization design technique for controller tuning is presented. This approach gives control engineers greater flexibility to select a controller that matches their specifications. Furthermore, for a given controller it is simple to analyze the tradeoff achieved between conflicting objectives. By using the multi-objective design technique it is also possible to perform a global comparison between different control strategies in a simple and robust way. This approach thereby enables an analysis to be made of whether a preference for a certain control technique is justified. This proposal is evaluated and validated in a nonlinear multiple-input multiple-output system using two control strategies: a classical proportional-integral-derivative control scheme and a feedback state controller.