Joaquin Carrasco

This letter investigates the problem of input-output synchronisation in a class of heterogeneous dynamical networks with nonlinear diffusive couplings in the presence of disturbances on the coupling links. Focusing on networks whose agent dynamics satisfy suitable relative dissipativity properties, distributed sufficient conditions are established to guarantee bounded edge disagreement in the presence of external disturbances. Specifically, these conditions can be verified using only local information associated with adjacent agents and coupling links. To illustrate the proposed results, a heterogeneous network of Goodwin oscillators is studied, and a numerical example further demonstrates the advantages of the proposed approach under network topology changes.

Dynamic multipliers can be used to guarantee the stability of Lurye systems with slope-restricted nonlinearities, but give no guarantee that the closed-loop system has finite incremental gain. We show that multipliers guarantee the closed-loop power gain to be bounded and quantifiable. Power may be measured about an appropriate steady state bias term, provided the multiplier does not require the nonlinearity to be odd. Hence dynamic multipliers can be used to guarantee such Lurye systems have low sensitivity to noise, provided other exogenous signals have constant steady state. For periodic excitation, the closed-loop response can apparently have a subharmonic or chaotic response. We revisit a class of multipliers that can guarantee a unique, attractive and period-preserving solution. We show the multipliers can be derived using classical tools and reconsider assumptions required for their application. Their phase limitations are inherited from those of discrete-time multipliers. The multipliers cannot be used at all frequencies unless the circle criterion can also be applied; this is consistent with known results about dynamic multipliers and incremental stability.

In this article, we address the critical challenge of vibration control of flexible long-reach robot manipulators used in nuclear decommissioning. The research is motivated by the urgent need to ensure precision and safety during the deployment of robotic systems in confined and hazardous environments, such as the through-wall deployment (TWD) system for the Sellafield nuclear site. The TWD system, featuring a rigid manipulator on a flexible two-link boom, is designed to maneuver through small openings in containment vessels. While this design avoids the need for bulky structures, the slenderness of the boom makes it prone to significant vibrations, potentially compromising the system’s stability and accuracy. To address these challenges, we propose a novel real-time flexible control system that suppresses vibrations using only the robot manipulator’s own actuation, without requiring additional actuators. The control strategy is based on the mixed-sensitivity $H_\infty$ synthesis for a dedicated dynamics model via inertial sensing, enhancing the robustness and adaptability over the multimodal flexibilities. Experimental validation demonstrated the control system’s effectiveness in reducing vibrations, thereby improving operational efficiency and safety. These findings have broader implications for deploying flexible, intelligent control systems in other high-stakes environments, such as the Fukushima Daiichi site, where similar vibration-related challenges are encountered.

In this work, the hard-constrained minimum principle based method for solving the inverse optimal control (IOC) problem has been considered. Specifically, this work investigates the kinds of closed-loop system trajectories, initial conditions and system dynamics for which a unique solution to the IOC problem can be obtained for this method. For this purpose, a matrix associated with the optimization problem involved in this IOC approach is tested for full rankness. It was found that for this method, in addition to initial conditions and types of closed-loop system trajectories, the open-loop system dynamics has an important role in determining if a unique solution to the IOC problem can be obtained. Rigorous mathematical and numerical analysis for different types of trajectories, initial conditions and system dynamics have been presented.

This article studies a mobile robot trajectory optimization problem where the control path constraints are affected by stochastic parameters and the obstacle information is limited. Based on online measured data, an upper confidence bound (UCB) is designed such that the estimated obstacle regions are guaranteed to cover the real obstacles with a predefined probability, thus avoiding collisions. Using the proposed approach, the control path constraints are transformed into deterministic constraints using analytic approximations. By adjusting the parameters in the proposed approximation function, the feasible set of the approximate optimization problem converges to the real feasible set conservatively. Such a property leads to both feasibility and suboptimality of the solution obtained by solving a deterministic optimization problem. Numerical results demonstrate that the designed UCB and approximation function are effective for trajectory optimization problems with control bounds and obstacle avoidance chance constraints. Comparative studies verified that the approximation function ensures the feasibility of the original chance constrained problem and reduces conservatism.

We consider Lurye systems, whose nonlinear operator is characterized by a nonlinearity that is bounded above and below by monotone functions. Absolute stability can be established using a subclass of the O'Shea-Zames-Falb multipliers. We develop phase conditions for both continuous-time and discrete-time systems under which there can be no such suitable multiplier for the transfer function of a given plant. In discrete time the condition can be tested via a linear program, while in continuous time it can be tested efficiently by exploiting convex structure. Results provide useful insight into the dynamic behaviour of such systems and we illustrate the phase limitations with examples from the literature.

Multipliers can be used to guarantee both the Lyapunov stability and input-output stability of Lurye systems with time-invariant memoryless slope-restricted nonlinearities. If a dynamic multiplier is used there is no guarantee the closed-loop system has finite incremental gain. It has been suggested in the literature that without this guarantee such a system may be critically sensitive to time-varying exogenous signals including noise. We show that multipliers guarantee the power gain of the system to be bounded and quantifiable. Furthermore power may be measured about an appropriate steady state bias term, provided the multiplier does not require the nonlinearity to be odd. Hence dynamic multipliers can be used to guarantee Lurye systems have low sensitivity to noise, provided other exogenous systems have constant steady state. We illustrate the analysis with an example where the exogenous signal is a power signal with non-zero mean.

In this paper, the solvability of the Inverse Optimal Control (IOC) problem based on two existing minimum principal methods, is analysed. The aim of this work is to answer the question regarding what kinds of trajectories, that is depending on the initial conditions of the closed-loop system and system dynamics, of the original optimal control problem, will result in the recovery of the true weights of the reward function for both the soft and the hard-constrained methods [1], [2]. Analytical conditions are provided which allow to verify if a trajectory is sufficiently conditioned, that is, holds sufficient information to recover the true weights of an optimal control problem. It was found that the open-loop system of the original optimal problem has a stronger influence on the solvability of the Inverse Optimal Control problem for the hard-constrained method as compared to the soft-constrained method. These analytical results were validated via simulation.