UC Riverside

This dissertation proposes communication-reduced solutions to the containment control, distributed average tracking and distributed time-varying optimization problems of multi-agent systems.

The objective of containment control in multi-agent systems is to design control algorithms for the followers to converge to the convex hull spanned by the leaders. Sampled-data based containment control algorithms are suitable for the cases where the power supply and sensing capacity are limited, due to their low-cost and energy-saving features resulting from discrete sensing and interactions. In addition, sampled-data control has advantages in performance, price and generality. On the other hand, when the agents have double-integrator dynamics and the leaders are dynamic with nonzero inputs, the existing algorithms are not directly applicable in a sampled-data setting. To this end, this dissertation proposes a sampled-data based containment control algorithm for a group of double-integrator agents with dynamic leaders with nonzero inputs under directed communication networks. By applying the proposed containment control algorithm, the followers converge to the convex hull spanned by the dynamic leaders with bounded position and velocity containment control errors, and the ultimate bound of the overall containment error is proportional to the sampling period. In the distributed average tracking problem, each agent uses local information to track the average of individual reference signals. In some practical applications, velocity measurements may be unavailable due to technology and space limitations, and it is also usually less accurate and more expensive to implement. Before deriving the event-triggered approach, we first present a base algorithm without using velocity measurements, which sets the stage for the development of the event-triggered algorithm. The base algorithm has an advantage over the existing related works in the senses that there is no global information requirement for parameter design. Building on the base algorithm, we present an event-triggered algorithm that further removes continuous communication requirement and is free of Zeno behavior. It is suitable for practical implementation since in reality the bandwidth of the communication network and power capacity are usually constrained. The event-triggered algorithm overcomes some practical limitations, such as the unbounded growth of the adaptive gain and requirement of additional internal dynamics, by constructing a new triggering strategy. In addition, a continuous nonlinear function is used to approximate the signum function to reduce the chattering phenomenon in reality.

In distributed optimization of networked systems, each member has a local cost function, and the goal is to cooperatively minimize the sum of all the local cost functions. The distributed time-varying optimization problem is investigated for networked Lagrangian systems with parametric uncertainties in the dissertation. Usually, in the literature, to address some distributed control problems for nonlinear systems, a networked virtual system is constructed, and a tracking algorithm is designed such that the agents' physical states track the virtual states. It is worth pointing out that such an idea requires the exchange of the virtual states and hence necessitates communication among the group. In addition, due to the complexities of the Lagrangian dynamics and the distributed time-varying optimization problem, there exist significant challenges. This dissertation proposes distributed time-varying optimization algorithms that achieve zero optimum-tracking errors for the networked Lagrangian agents without the communication requirement. The main idea behind the proposed algorithms is to construct a reference system for each agent to generate a reference velocity using absolute and relative physical state measurements with no exchange of virtual states needed, and to design adaptive controllers for Lagrangian systems such that the physical states are able to track the reference velocities and hence the optimal trajectory. The algorithms introduce mutual feedback between the reference systems and the local controllers via physical states/measurements and are amenable to implementation via local onboard sensing in a communication unfriendly environment. Specifically, first, a base algorithm is proposed to solve the distributed time-varying optimization problem for networked Lagrangian systems under fixed graph. Then, based on the base algorithm, a continuous function is introduced to approximate the signum function, forming a continuous distributed optimization algorithm and hence removing the chattering. Then, by using the structure of the base algorithm, a distributed time-varying optimization algorithm is designed for networked Lagrangian systems under switching graphs.