Zhiyong Geng

Adaptive output feedback consensus tracking for linear multi-agent systems with unknown dynamics

In this paper, the consensus tracking problem with unknown dynamics in the leader for the linear multi-agent systems is addressed. Based on the relative output information among the agents, decentralised adaptive consensus protocols with static coupling gains are designed to guarantee that the consensus tracking errors converge to a small neighbourhood around the origin and all the signals in the closed-loop dynamics are uniformly ultimately bounded. Moreover, the result is extended to the case with dynamic coupling gains which are independent of the eigenvalues of the Laplacian matrix. Both of the protocols with static and dynamic coupling gains are designed by using the relative outputs, which are more practical than the state-feedback ones. Finally, the theoretical results are verified through an example.

Robust stability of the systems with mixed uncertainties under the IQC descriptions

This paper studies the problem of robust stability checking for a single-input single-output uncertain feedback system which consists of a linear uncertain plant in the forward loop and a non-linear dynamic uncertain unit in the feedback loop. It is supposed that the linear part of the system is of parametric uncertainties described by a polytopic perturbation mode, and that the non-linear part of the system is of dynamic uncertainties characterized by an integral quadratic constraint (IQC). The problem of stability checking is discussed for different structures of the IQC multiplier based on the concepts of biconvex and convex-concave functions and their properties. For different uncertainty structures of the system, a finite vertex checking result and an edge checking result are presented. As an application of the above results, the problem of robust H performance checking is discussed for the case that the uncertain plant of a feedback system is parameterized by a polytopic perturbation mode, and an edge checking result is given under a fairly mild assumption. Also, the absolute stability of an interval system is investigated, and the vertex results of circle criterion and Popov criterion are obtained. Finally, a demonstrating example is included.

Robust analysis and synthesis for the gradient-like behaviour of uncertain pendulum-like systems

This paper focuses on uncertain pendulum-like systems subject to norm constraint structured uncertainties, and addresses the robust gradient-like behaviour analysis and synthesis problems for such systems. By applying the structured singular value of an operator to structured uncertainty, the results on robust analysis for the gradient-like behaviour of uncertain pendulum-like systems are obtained. Based on the analysis results, using KYP lemma, a dynamic output feedback controller for the closed loop system guaranteeing gradient-like behaviour is designed and the controller parameters are explicitly expressed by a set of feasible solutions of corresponding linear matrix inequalities. Finally two numerical examples are presented to demonstrate the applicability and validity of the proposed approach.

Stability analysis for the systems with feedback norm constraint uncertainties

This paper considers the problem of Lp stability checking for a feedback uncertain system which consists of a linear plant in its forward loop and non-linear uncertain dynamics in its feedback loop. It is supposed that the non-linear part of the system is of dynamic uncertainties characterized by a certain set of constraints. The concepts used here are the well-posedness of the feedback system and the norm constraint for the feedback uncertainties, leading to a sufficient condition for robust stability. The result is illustrated to be efficient through an example.

Self-Balancing Controlled Lagrangian and Geometric Control of Unmanned Mobile Robots

This work presents a novel geometric framework for self-balancing as well as planar motion control of wheeled vehicles with two fewer control inputs than the configuration variables. For self-balancing control, we shape the kinetic energy in such a way that the upright direction of the robot’s body becomes a nonlinearly stable equilibrium for the corresponding controlled Lagrangian which is inherently a saddle point. Then for planar motion control of the robot, we set its position and attitude as an element of the special Euclidean group SE(2) and apply a logarithmic feedback control taking advantage of the Lie group exponential coordinates. For simulation and evaluating the controllers, the unified dynamic model of the self-balancing mobile robot (SMR) is developed using the constrained Euler-Lagrange equations.

Design of controller for Lur'e systems guaranteeing dichotomy

In this paper, the problem of controller design for Lur’e systems guaranteeing dichotomy is investigated. On the basis of Kalman–Yakubovich–Popov (KYP) lemma and two frequency equalities, a new methodology for the dichotomy analysis of the Lur’e systems is proposed. A linear matrix inequality (LMI) based criterion is derived, which is equivalent to the Leonov’s frequency-domain one, while for the dichotomy analysis and synthesis which is more straightforward than the frequency-domain one. In virtue of this result, a dynamic output feedback controller ensuring the dichotomy property for Lur’e systems is designed. Finally a numerical example is included to demonstrate the validity and the applicability of the proposed approach.

Stabilisation of a relative equilibrium of an underactuated AUV on SE(3)

ABSTRACT This paper presents stabilisation of a relative equilibrium of an underactuated autonomous underwater vehicle (AUV) with three independent control inputs on Lie group SE(3), since SE(3) can describe the evolution of a rigid body without singularities or ambiguities. First, by using the interconnection and damping assignment (IDA) method through kinetic energy shaping, a controller is proposed to stabilise the relative equilibrium in the sense of Lyapunov stability in cotangent bundle T * SE(3) modulo an isotropy subgroup when a marine vehicle immerses in an ideal fluid. Then, for an AUV submersed in a viscous fluid, an asymptotical static control law consisting of three terms is designed to stabilise the relative equilibrium via the IDA method, which these three control terms are derived from kinetic energy shaping, potential energy shaping and damping reassignment, respectively. The control term derived from kinetic energy shaping preserves stability of this motion modulo translations along the shortest semi-axis in any direction and rotations about the same axis. Moreover, the static controller is developed to a dynamic one via adaptive neural network approach, which is robust for uncertainties in the systems damping and mass. Simulation results complete our work.

Logarithmic control, trajectory tracking, and formation for nonholonomic vehicles on Lie group SE(2)

ABSTRACT This paper studies the problem of set-point stabilisation, trajectory tracking, and formation tracking for unicycle-type vehicles by taking advantage of the exponential coordinates and the other mathematical tools provided by the Lie group setting of the special Euclidean group SE(2). Motivated by recent developments in geometric control approaches for holonomic systems, we first study the stabilisation problem for nonholonomic constrained kinematic systems by improving the logarithmic stabilising control laws in such a way that they can satisfy nonholonomic constraints too. We then extend the control design to the problem of trajectory tracking by proposing auxiliary systems and investigating the conditions for which the adjoint map in the Lie algebra preserves the velocity constraint. This leads to a global control law which is valid for general time-varying as well as non-smooth trajectories. The tracking control law is also applied to the problem of leader-follower formation tracking by constructing nonholonomic virtual leaders in the desired formation. Finally, the kinematic control law is translated to a differential drive robot using the backstepping technique. To demonstrate the effectiveness of the controllers, the numerical results are presented and the performances are compared with the other three controllers in the literature.

The geometric convexity on SE(3) and its application to the formation tracking in multi-vehicle systems

ABSTRACT This paper considers the problem of geometric convexity on special Euclidean group SE(3) and its application to the formation tracking in multi-vehicle systems. Motivated by the convex hull on Euclidean space, the specific expression of geodesic connecting two points on SE(3) is obtained based on the Pontryagins Minimum Principle. Then it is extended to the geometric convex combination for multiple points, based on which the virtual systems on SE(3) is given to be used in the application of formation tracking problem. In light of the geometric convex combination and virtual systems on SE(3), a consensus-based tracking protocol is proposed to guarantee that the formation is achieved under the directed acyclic graphs. Finally, two numerical examples are provided to demonstrate the validity of the theoretical results.