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We present an adaptive algorithm that guarantees synchronization in diffusively-coupled systems. We first consider compartmental systems of ODEs where variables in each compartment are interconnected through diffusion terms with like variables in other compartments. Each set of variables may have its own weighted undirected graph describing the topology of the interconnection between compartments...
In this paper, three dimensional impact angle control guidance laws are proposed for stationary targets. Unlike the usual approach of decoupling the engagement dynamics into two mutually orthogonal 2-dimensional planes, the guidance laws are derived using the coupled dynamics. These guidance laws are designed using principles of conventional as well as nonsingular terminal sliding mode control theory...
We present a numerical investigation of the performance of retrospective cost adaptive control (RCAC) for spacecraft attitude control using control-moment-gyroscopes (CMG). The setup consists of three orthogonally mounted CMG's that are velocity commanded without the use of a steering law. RCAC is applied in a decentralized architecture; each CMG is commanded by an independent RCAC control laws. This...
Parameter dependent systems are found in many complex coupled systems. When applying optimization techniques, using full order models for the solution of parameter dependent systems may simply be intractable. Therefore we investigate methods for generating reduced order models that can be applied to nonlinear parameter dependent systems. The development of these reduced order models is made possible...
The problem of multi-objective feedback controller design of nonlinear systems is solved in this paper. The T-S fuzzy model is adopted to describe the nonlinear systems and genetic algorithm is used to identify the T-S fuzzy model. The identified T-S fuzzy model is reduced by applying Higher Order Singular Value Decomposition (HOSVD) method. Based on the reduced T-S fuzzy model, an optimal state feedback...
In this paper, the error observer linearization is extended to a class of observable cascade systems which contains state affine systems up to output injection. First, we give a theoretical result which states necessary and sufficient conditions. Next, we give an algorithm permitting to calculate a system of coordinates in which a nonlinear system takes the desired cascade observable form.
In this paper, we study the finite-time consensus problem of networked nonlinear systems under directed fixed graph. A nonlinear system is considered as a controlled first-order differential equation with/without drift term commonly used to model autonomous systems. For multi-system formation under directed fixed graph, a protocol is proposed to solve consensus problems in finite time. Guided by finite-time...
This paper is devoted to computation of flat outputs by means of the Goursat normal form of the Pfaffian system associated to any control system in state space form. The algorithm explained here consists in three steps: i) Transformation of the system into its Pfaffian equivalent. ii) Computation of the Goursat normal form for the Pfaffian system. iii) Rewriting of the state space equations in the...
An integral part of the CPA method to compute Continuous and Piecewise Affine Lyapunov functions for nonlinear systems is the generation of a suitable triangulation. Recently, the CPA method was revised by using more advanced triangulations and it was proved that it can compute a CPA Lyapunov function for any nonlinear system possessing an exponentially stable equilibrium. This more advanced triangulation...
This paper proposes to control a class of nonlinear systems described by the discrete-time nonlinear ARX models with unknown parameters depending on the input and output. A set of adaptive controllers are designed based on the variable structure control for the discrete-time ARX models locally identified around given levels of input and output. The proper adaptive controller is chosen among the set...
Robustness of nonlinear systems can be analyzed by computing robust forward invariant sets (RFIS). The smallest RFIS provides the least conservative estimate of system performance under perturbations. However, computation of the smallest RFIS through brute force search can be a difficult task. We develop a novel algorithm to find the smallest RFIS for two-dimensional systems subjected to bounded additive...
In this paper we propose a nonlinear H2 control to improve transient response in the position control and to reduce energy consumption for the position tracking of Sawyer motors. The proposed method consists of a nonlinear torque modulation with a commutation scheme and gain scheduling LPV controller. The position control problem for the Sawyer motor is reformulated into the LPV system optimal problem...
In this paper, we study the controllability of nonlinear networked systems. In particular, we describe how graph symmetries combined with dynamic symmetries result in a loss of controllability in nonlinear leader-follower networks. Our result generalizes those of Rahmani et al. (2009) who considered the case of a linear consensus-type dynamics, namely the unweighted Laplacian network flow. We consider...
A nonlinear current-mode proportional-integral (PI) controller is proposed for the challenging problem of regulating the output voltage of a dc/dc boost power converter. For the analysis, the accurate average nonlinear model of the boost converter is used, while a new advanced passivity-based nonlinear stability analysis is applied. Particularly, it is firstly proven that the closed-loop system is...
In this paper a convergent, nearest-neighbor, consensus control protocol is suggested for agents with nontrivial dynamics. The protocol guarantees convergence to a common point in space even if each agent is restricted to communicate with its nearest neighbor. The neighbor, however, is restricted to lie outside an arbitrarily small priority zone surrounding the agent. The control protocol consists...
In this paper, we deal with the problem of obtaining a state feedback controller for polynomial dynamical systems such that the resulting closed-loop system will have a prescribed vector field on a given algebraic set. The problem relates to the realization of a prescribed stable limit cycle and the path following control. A procedure for solving the problem is provided such that all the polynomial...
In this paper, we design a distributed dynamic feedback controller that implements real-time economic optimization in power networks with tree topology. We consider the coupling between the dynamics of the power network and the appropriately formulated optimization problem in the real-time market, i.e., when the time-scale separation between markets and network dynamics fades. The design methodology...
In this paper a nonlinear attitude tracking control scheme is developed for a small-scaled unmanned helicopter under input constraints. Via the analysis of the properties associated with the helicopter's rotor dynamics, the elevator servo input, the aileron servo input, and the rudder servo input are chosen to be the control inputs to be designed. Their constraints in amplitude under hovering flight...
This paper presents a robust performance analysis result for a class of uncertain quantum systems containing sector bounded nonlinearities arising from perturbations to the system Hamiltonian. An LMI condition is given for calculating a guaranteed upper bound on a non-quadratic cost function. This result is illustrated with an example involving a Josephson junction in an electromagnetic cavity.
This paper investigates the problem of fault estimation and fault tolerant control for a class of Lipschitz nonlinear systems, which are subjected simultaneously to sensor faults and uncertainties. By taking the sensor faults as auxiliary states, an augmented system is constructed. For this system, an unknown input observer (UIO) with ℋ∞ performance criterion is first developed to simultaneously estimate...
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