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This paper first investigates the challenging graph theoretic problem of constructing universally rigid tensegrity frameworks given any generic configuration. We design a numerical algorithm to construct a universally rigid tensegrity framework, such that the resulted eigenvalues of the stress matrix of the tensegrity framework can be selected beforehand. As one application, we then consider the formation scaling problem for multi-agent systems, in which the agents and their interaction relationship are respectively represented by the nodes and the underlying graph of the tensegrity framework. Distributed control laws are developed using the stresses, which render the global exponential convergence to the target formation shape. We also carry out several simulations to validate the theoretical results.

A continuous stirred tank reactor (CSTR) is typical of equipment found in the process control industry. The dynamics represent a wide class of second order nonlinear systems and thus as well as having specific industrial application, control of the CSTR is frequently used as a benchmark problem for application and testing of new control algorithms. Due to the high complexity of the CSTR system, the robust control design problem is challenging. This paper first establishes a mathematical model of the system. A disturbance observer is then designed to estimate the disturbance and a corresponding asymptotically stable sliding mode control is developed. Stability analysis is presented in terms of the Lyapunov method. Finally, based on experimental data, the proposed method is validated using simulation experiments.

For the solution of optimal control problem involving an index-1 differential-algebraic equation, an efficient function evaluation algorithm is proposed in this paper. In the evaluation procedure, the state equation is propagated forwards, then, adjoint sensitivity is propagated backwards. Thus, it is computationally more efficient than forward sensitivity propagation when the number of constraints is less than that of optimization variables. In order to reduce Newton iterations, the adjoint sensitivity is derived utilizing the implicit function theorem, and the integration procedure is accelerated by incorporating a predictor-corrector strategy. This algorithm is integrated with a nonlinear programming solver Ipopt to solve sequentially the point-to-point optimal control for a Delta robot with constrained motor torque. Numerical experiments demonstrate the efficiency of this algorithm.

In this paper we study rendezvous control of multiple mobile robots. We propose a control law that merely requires each robot to measure the relative bearings of their neighbors in their local coordinate frames. Distance measurement or relative position estimation is not required. In theory, the proposed control law verifies that distance information is redundant in rendezvous control tasks though the objective of rendezvous is to decrease the inter-robot distances. In practice, the control law provides a simple solution to vision-based rendezvous tasks where bearings can be measured by visual sensing. Moreover, we generalize the proposed control law by introducing an additional heading vector into the control law. This heading vector may preserve the system convergence and, in the meantime, provides great flexibility to adapt the control law for nonholonomic robot models or obstacle avoidance.

This paper proposes an incipient sensor fault detection method for three-phase PWM inverter devices in electric railway traction systems. An adaptive and sliding mode unknown input observer is designed for sensor faulty inverter system. The invariant ellipsoid is used to generate threshold. The parameters of the observer are particularly designed such that the estimation errors converge to the threshold invariant ellipsoid before the sensor fault develops to incipient fault degree, and the estimation errors exceed the threshold after the sensor fault develops to incipient fault degree. Finally, simulations based on the traction system in CRH2 (China Railway High-speed) are presented to verify the effectiveness of the proposed method.

This paper proposes a robust fault detection observer based on zonotopes for discrete-time uncertain systems with sensor faults and unknown but bounded uncertainties. The main advantage of this method is that the observer gain of the robust zonotopic observer is designed to be robust against bounded uncertainties while being sensitive to faults. In order to detect sensor faults with low magnitudes, the fault sensitivity is taken into account by measuring the H − performance. The designed zonotopic observer gain can be obtained by solving an optimization problem including a sequence of linear matrix inequalities (LMIs). Finally, an illustrative example is provided to demonstrate the proposed method.