Decentralized variable structure control design for a two-pendulum system

This note presents a decentralized variable structure control design for a nonlinear state model of two coupled pendulums. This was motivated by the swing equation model of a two-machine power system whose behavior is similar. The control objective is to drive the pendulum motion from one equilibrium point to another.     

An example of a nonlinear regulator

The purpose of this note is to use the concept of feedback equivalence to linear controllable systems in order to design a nonlinear regulator for a synchronous generator connected to an infinite bus. The design of the regulator will show how recently developed theorems in the area of geometric nonlinear control theory approach a power system problem, offering an interesting solution.     

Adaptive stabilization of a class of nonlinear systems with unstable internal dynamics

This note considers global stabilization of a class of uncertain nonlinear output feedback systems with unstable internal dynamics. The coefficients which characterize the internal dynamics are allowed to be functions of system output, and the uncertainty of the system is characterized by an unknown constant parameter vector. The key step in the proposed control design is to estimate the internal state variables and impose control over them. The control design is presented first for systems without unknown parameters, and then for the systems with unknown parameters using adaptive control techniques.     

Exact design manifold control of a class of nonlinear singularly perturbed systems

The integral manifold approach captures from a geometric point of view the intrinsic two-time-scale behavior of singularly perturbed systems. An important class of nonlinear singularly perturbed systems considered in this note are fast actuator-type systems. For a class of fast actuator-type systems, which includes many physical systems, an explicit corrected composite control, the sum of a slow control and a fast control, is derived. This corrected control will steer the system exactly to a required design manifold.     

Parallel Optimal Control for Weakly Coupled Nonlinear Systems Using Successive Galerkin Approximation

This technical note presents a new algorithm for the closed-loop parallel optimal control of weakly coupled nonlinear systems with respect to performance criteria using the successive Galerkin approximation (SGA). By using the weak coupling theory, the optimal control law can be obtained from two reduced-order optimal control problems in parallel, but the resulting problem is difficult to solve for nonlinear systems. In order to overcome the difficulties inherent in the nonlinear optimal control problem, the parallel optimal control laws are constructed in terms of the approximated solutions to two independent Hamilton-Jacobi-Bellman equations using the SGA method. One of the purposes of this note is to design the closed-loop parallel optimal control law for the weakly coupled nonlinear systems using the SGA method. The second is to reduce the computational complexity when the SGA method is applied to the high-order weakly coupled systems.      

非线性相似组合系统的鲁棒输出跟踪控制*

研究一类具有相似结构的非线性不确定组合系统的分散输出跟踪控制问题,利用的相似结构,提出一种设计具有相似结构的分散滑模控制器的方法,所设计的控制器,对于所有允许的不确定性,均使系统输出渐近跟踪所给定的参考输出。     

Circle-criterion Based Nonlinear Observer Design for Sensorless Induction Motor Control

This paper deals with the design of a nonlinear observer for sensorless induction motor control. Based upon the circle criterion approach, a nonlinear observer is designed to estimate pertinent but unmeasurable state variables of the considered induction machine for sensorless control purpose. The observer gain matrices are computed as a solution of linear matrix inequalities(LMI) that ensure the stability conditions of the state observer error dynamics in the sense of Lyapunov concepts. Measured and estimated state variables can be exploited to perform a state feedback control of the machine system. The simulation results are presented to illustrate the effectiveness of the proposed approach for nonlinear observer design.     

Less conservative conditions for asymptotic stability of impulsive control systems

This note studies the stability of impulsive control systems. A new comparison theorem for asymptotic stability of impulsive differential system is presented. Based on the new result, we derive some less conservative conditions for asymptotic stability of impulsive control systems with impulses at fixed times and the results are used to design impulsive control for a class of nonlinear systems. The class of nonlinear systems considered is also enlarged.     

Observer-based dynamic surface control for a class of nonlinear systems: an LMI approach

This note presents a new analysis method to design an observer-based dynamic surface controller (ODSC) for a class of nonlinear systems. While the separation principle from linear system theory does not generally hold for nonlinear systems, a separation principle for the ODSC systems will be shown for a class of nonlinear systems, thus enabling the independent design of the observer and DSC. Furthermore, a convex optimization problem to test quadratic stability of ODSC will be formulated later.     

A flat-zone modification for robust adaptive control of nonlinearoutput feedback systems with unknown high-frequency gains

This note deals with adaptive control of perturbed nonlinear output feedback systems with unknown high-frequency gains. The disturbances in the systems are assumed to be bounded, but the bounds are unknown. A flat-zone modification is proposed to incorporate both the bound estimation and Nussbaum gain design in the nonlinear adaptive control. To ensure the differentiability of stabilizing functions needed for backstepping design, high order terms are introduced in the Lyapunov function candidate with a flat zone around the neighborhood of the origin. The output tracking error converges to an arbitrarily small interval around zero     

Quadratic stabilizability of uncertain linear systems: Existence of a nonlinear stabilizing control does not imply existence of a linear stabilizing control

This note is concerned with the problem of stabilizing an uncertain linear system via state feedback control. An uncertain system which admits a stabilizing state feedback control and some associated quadratic Lyapunov function is said to be quadratically stabilizable. In a number of recent papers, conditions are given under which quadratic stabilizability via nonlinear control implies quadratic stabilizability via linear control. These papers restrict the manner in which the uncertain parameters are permitted to enter structurally into the state equation in order to establish this result. This note presents an example which shows that this implication is not true for more general uncertain linear systems. To this end, we describe an uncertain linear system which is quadratically stabilizable via nonlinear control but not quadratically stabilizable via linear control.     

State feedback stabilization for a class of stochastic time-delay nonlinear systems

This note focuses on a class of stochastic time-delay nonlinear systems. The problem we address is to design a controller such that the closed-loop system is exponentially stable. It is shown that the stabilization via state feedback can be solved by a Lyapunov-based recursive design method.     

Input linearization of nonlinear systems via pulse-width control

In this note, it is shown that a general nonlinear system can be transformed to an affine nonlinear system by virtue of the use of pulsewidth control. Therefore, the combined system from the pulse width control input to the nonlinear system output behaves as an affine (linear-in-control) system. By this way, a cumbersome nonlinear system model can be transformed to a simpler linear-in-control form without increasing the system dimension; this in turn enables simpler control design. Furthermore, using this methodology, some control design methods developed only for affine systems can be adapted to general nonlinear systems.     

Output feedback stabilization for a class of stochastic time-delay nonlinear systems

This note focuses on a class of stochastic time-delay nonlinear systems. The problem we address is to design a controller such that the closed-loop system is exponentially stable. It is shown that the stabilization via output feedback can be solved by a Lyapunov-based recursive design method.     

Global finite-time stabilization by dynamic output feedback for a class of continuous nonlinear systems

This note studies the problem of global finite-time stabilization by dynamic output feedback for a class of continuous but nonsmooth nonlinear systems. By extending the adding-a-power-integrator technique and a special continuous observer design, a dynamic output feedback controller is explicitly constructed to render the systems globally finite-time stable. The novelty of the note is the development of a recursive design procedure, which takes full advantage of the continuous structure of the systems in constructing the state feedback stabilizer and the continuous observer with rigorously selected gains.     

Fault-tolerant control of a class of asynchronous sequential machines with permanent faults

In this note, we address a fault-tolerant control scheme for asynchronous sequential machines with permanent faults. The considered asynchronous machine is influenced by faults that change perpetually a portion of its state transition logic. If the asynchronous machine has appropriate analytic redundancy in its reachability, we can design a corrective controller so that the stable-state behavior of the closed-loop system can match that of a reference model despite occurrences of permanent faults. It is assumed that the controller is always fault-free. The existence condition and design procedure for an appropriate controller are presented based on the corrective control scheme. We also provide a controller synthesis example for validating the proposed scheme.     

Operator-based nonlinear feedback control design using robust right coprime factorization

In this note, robust stabilization and tracking performance of operator based nonlinear feedback control systems are studied by using robust right coprime factorization. Specifically, a new condition of robust right coprime factorization of nonlinear systems with unknown bounded perturbations is derived. Using the new condition, a broader class of nonlinear plants can be controlled robustly. When the spaces of the nonlinear plant output and the reference input are different, a space change filter is designed, and in this case this note considers tracking controller design using the exponential iteration theorem.     

Direct adaptive control for a class of MIMO nonlinear systems using neural networks

In this note, direct adaptive neural network (NN) control is studied for a class of multiple-input-multiple-output nonlinear systems based on input-output discrete-time model with unknown interconnections between subsystems. By finding an orthogonal matrix to tune the NN weights, the closed-loop system is proven to be semiglobally uniformly ultimately bounded. The control performance of the closed-loop system is guaranteed by suitably choosing the design parameters.     

An output feedback precompensator for nonlinear DAE systems with control-dependent state-space

This note considers singular systems of nonlinear differential and algebraic equations (DAEs) whose constrained state space depends on the control inputs. A state-space realization of such systems cannot be derived independently of the controller design. An output feedback precompensator is derived, which results in a modified DAE system whose state-space is invariant under any feedback control law and can be used for output feedback controller synthesis. Its application is illustrated by a nonlinear electrical circuit example.     

Output feedback control design for strict-feedback stochastic nonlinear systems under a risk-sensitive cost

In this note, we study the problem of output-feedback control design for a class of strict feedback stochastic nonlinear systems. Under an infinite-horizon risk-sensitive cost criterion, the controller designed can guarantee an arbitrary small long-term average cost for arbitrary risk-sensitivity parameter and achieve boundedness in probability for the closed-loop system, using the integrator backstepping methodology. Furthermore, the controller preserves the equilibrium at the origin of the nonlinear system.