On the backstepping design procedure for multiple input nonlinear systems

Recently, we developed a structural decomposition for multiple input multiple output nonlinear systems that are affine in control but otherwise general. This structural decomposition simplifies the conventional backstepping design and allows a new backstepping design procedure that is able to stabilize some systems on which the conventional backstepping is not applicable. In this paper we further exploit the properties of such a decomposition for the purpose of solving the semi-global stabilization problem for minimum phase nonlinear systems without vector relative degrees. By taking advantage of special structure of the decomposed system, we first apply the low gain design to the part of system that possesses a linear dynamics. The low gain design results in an augmented zero dynamics that is locally stable at the origin with a domain of attraction that can be made arbitrarily large by lowering the gain. With this augmented zero dynamics, backstepping design is then applied to achieve semi-global stabilization of the overall system.

This work proposes a discrete-time non-linear neural observer based on a recurrent high order neural network in parallel model trained with an algorithm based on the extended Kalman filter for discrete-time multiple input multiple output non-linear systems with unknown dynamics and unknown time-delay. To prove the semi-globally uniformly ultimately boundedness of the proposed neural observer the stability analysis based on the Lyapunov approach is included. Applicability of the proposed observer is shown via simulation and experimental results.

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

Control of MIMO nonlinear systems: A data-driven model inversion approach

SummaryThis paper studies the problem of adaptive fuzzy asymptotic tracking control for multiple input multiple output nonlinear systems in nonstrict‐feedback form. Full state constraints, input quantization, and unknown control direction are simultaneously considered in the systems. By using the fuzzy logic systems, the unknown nonlinear functions are identified. A modified partition of variables is introduced to handle the difficulty caused by nonstrict‐feedback structure. In each step of the backstepping design, the symmetric barrier Lyapunov functions are designed to avoid the breach of the state constraints, and the issues of overparametrization and unknown control direction are settled via introducing two compensation functions and the property of Nussbaum function, respectively. Furthermore, an adaptive fuzzy asymptotic tracking control strategy is raised. Based on Lyapunov stability analysis, the developed control strategy can effectually ensure that all the system variables are bounded, and the tracking errors asymptotically converge to zero. Eventually, simulation results are supplied to verify the feasibility of the proposed scheme.

Higher order nonlinear systems with prevailing delay have been very challenging in significance with stability and process performance. This paper investigates the performance of a type-2 Mamdani intelligent controller implemented a delay dominant system which is modelled using black box approach identified to be a second order nonlinear model for a dual spherical tank liquid level system (DSTLLS) under LabVIEW environment. The adaptive approach of the intelligent Mamdani-based fuzzy controller proves itself to be very competent compared with the earlier experimented methods that already exist. The performance indices like integrated absolute error (IAE) and integrated squared error (ISE) are also calculated for different varying set point changes of DSTLLS. The response and error reduction efficiency of this method of adaptive type-2 intelligent fuzzy (ATIF) controller has been experimented for different flow configurations of this DSTLLS, like multiple input single output (MISO), multiple input multiple output (MIMO) and single input single output (SISO).

This paper presents a new method for modelling of dynamic systems by using specially designed orthogonal polynomial neural networks. These networks utilize the feature that the basis made of orthogonal functions can be used for approximation of arbitrary function, while their property of orthogonality enables optimal performances in the sense of both convergence time and approximation error. In this regard, generalized quasi-orthogonal polynomials, specifically tailored for the application in the modelling of complex dynamic systems with time-varying behaviour, are considered. Adaptivity of the designed model is achieved by using variable factors inside the orthogonal basis. The designed orthogonal neural network is applied in modelling of laboratory twin-rotor aero-dynamic system as a representative of nonlinear multiple input-multiple output systems. Detailed comparative analysis is performed for a different number of polynomials in expansion with the purpose of finding the optimal model in the sense of trade-off between model accuracy and complexity.

This work proposes a method to construct a state-shared model for multiple-input multiple-output (MIMO) systems. A state-shared model is defined as a linear time invariant state-space structure that is driven by measurement signals-the plant outputs and the manipulated variables, but shared by different multiple input/output models. The genesis of the state-shared model is based on a particular reduced non-minimal realization. Any such realization necessarily fulfills the requirement that the output of the state-shared model is an asymptotically correct estimate of the output of the plant, if the process model is selected appropriately. The approach is demonstrated on a nonlinear MIMO system — a physiological model of calcium fluxes that controls muscle contraction and relaxation in human cardiac myocytes.

Fixed-time resource allocation algorithm for high-order MIMO nonlinear multi-agent systems

This chapter proposes a servo control of multiple-input multiple-output (MIMO) nonlinear systems approximated by piecewise bilinear (PB) models. The approximated model is found to be fully parametric. The input-output (I/O) feedback linearization is applied to stabilize PB control systems. The controller can be represented as a Look-Up-Table (LUT). We apply the servo control based on PB models to the Caltech ducted fan model. Although the controller is simpler than the conventional I/O feedback linearizing controller, the control performance based on PB model is the same as the conventional one. The example is shown to confirm the feasibility of our proposals by computer simulations.

An adaptive system for linear systems with unknown parameters is a nonlinear system. The analysis of such adaptive systems requires similar techniques to analyse nonlinear systems. Therefore it is natural to treat adaptive control as a part of nonlinear control systems. Nonlinear and Adaptive Control Systems treats nonlinear control and adaptive control in a unified framework, presenting the major results at a moderate mathematical level, suitable for MSc students and engineers with undergraduate degrees. Topics covered include introduction to nonlinear systems; state space models; describing functions for common nonlinear components; stability theory; feedback linearization; adaptive control; nonlinear observer design; backstepping design; disturbance rejection and output regulation; and control applications, including harmonic estimation and rejection in power distribution systems, observer and control design for circadian rhythms, and discrete-time implementation of continuous-time nonlinear control laws.

This paper advances a neural-network-based approximate dynamic programming control mechanism that can be applied to complex control problems such as helicopter flight control design. Based on direct neural dynamic programming (DNDP), an approximate dynamic programming methodology, the control system is tailored to learn to maneuver a helicopter. The paper consists of a comprehensive treatise of this DNDP-based tracking control framework and extensive simulation studies for an Apache helicopter. A trim network is developed and seamlessly integrated into the neural dynamic programming (NDP) controller as part of a baseline structure for controlling complex nonlinear systems such as a helicopter. Design robustness is addressed by performing simulations under various disturbance conditions. All designs are tested using FLYRT, a sophisticated industrial scale nonlinear validated model of the Apache helicopter. This is probably the first time that an approximate dynamic programming methodology has been systematically applied to, and evaluated on, a complex, continuous state, multiple-input multiple-output nonlinear system with uncertainty. Though illustrated for helicopters, the DNDP control system framework should be applicable to general purpose tracking control.

Operator based nonlinear vibration control design for a multiple input multiple output(MIMO) wing-plate system is considered. For considering the MIMO wing-plate system with the effect of the coupling from the piezoelectric actuator(PEA)'s moments, the bounded input bounded output(BIBO) stability of the system is considered based on operator theory. Simultaneously, for obtaining the desired vibration control performance, the operators are designed to compensate for the external force and coupling's effects. Finally, the effectiveness of the designed nonlinear control system is confirmed by the numerical simulation.

Teaching Aids for Laboratory Experiments with AR.Drone2 Quadrotor

An advanced reconfigurable controller enhanced by a multiple model architecture is proposed as a tool to achieve fault tolerance in complex nonlinear systems. The most complete adaptive critic design, globalized dual heuristic programming (GDHP), constitutes a highly flexible nonlinear adaptive controller responsible for the generation of new control solutions for novel plant dynamics introduced by unknown faults. The main contribution of the presented work focuses on a novel fault tolerant control supervisor. Working on a higher hierarchical level, the proposed supervisor makes use of two quality indices to perform fault detection, identification and isolation based on the knowledge stored in a dynamic model bank (DMB). In the event of abrupt known faults, such knowledge is then used to greatly reduce the reconfiguration time of the GDHP controller. The synergy of the proposed supervisor and GDHP goes beyond, as solutions designed by the controller to previously unknown faults are autonomously added to the model bank. The fine interrelations between the algorithm's subsystems and its advanced capabilities are illustrated through extensive numerical simulations of a single-input single-output (SISO) linear system and of a multiple-input multiple-output (MIMO) nonlinear system, both subject to a series of fault scenarios involving expected and unexpected, abrupt and incipient faults. Note to Practitioners-The raising complexity of physical plants and control missions inevitably leads to increasing occurrence, diversity and severity of faults. Take automated production process as an example, the extent of time a plant is capable of maintaining acceptable performance levels is now considered to be the single factor with the highest impact on profitability. For a growing number of plants, it has become impractical to list all possible fault scenarios in order to take the necessary steps to assure continuous healthy operation. Therefore, it is now essential to have a control algorithm dedicated to the provision of tailored control solutions capable of maintaining stability and as much performance as possible during the occurrence of faults. This is the goal of fault tolerant control. In the presented paper, the most complete adaptive critic design, globalized dual heuristic programming (GDHP), is responsible for the generation of new control solutions for novel plant dynamics introduced by faults unknown at design time. A highly flexible nonlinear adaptive controller, GDHP is capable of dealing with both abrupt and incipient (gradually changing dynamics) faults. Working on a higher hierarchical level, a novel fault supervisor is introduced which makes use of two quality indices to perform fault detection, identification and isolation based on the knowledge stored in a dynamic model bank (DMB). In the event of abrupt known faults, such knowledge is then used to greatly reduce the convergence time of the GDHP controller. The synergy of the proposed supervisor and GDHP goes further, as solutions designed by the controller to previously unknown faults are autonomously added to the model bank in fact allowing the supervisor to learn new fault scenarios and their solutions as they occur. The fine interrelations between the algorithm's subsystems and its advanced capabilities are illustrated through extensive numerical simulations.