Dwaipayan Mukherjee

Generalization of deviated linear cyclic pursuit

Earlier work on cyclic pursuit systems has shown that using heterogeneous gains for agents in linear cyclic pursuit, the point of convergence (rendezvous point) can be chosen arbitrarily. But there are some restrictions on this set of reachable points. The use of deviated cyclic pursuit, as discussed in this paper, expands this set of reachable points to include points which are not reachable by any known linear cyclic pursuit scheme. The limits on the deviations are determined by stability considerations. Such limits have been analytically obtained in this paper along with results on the expansion in reachable set and the latter has also been verified through simulations.

Deviated linear cyclic pursuit

This paper analyses deviated linear cyclic pursuit in which an agent pursues its leader with an angle of deviation in both the continuous- and discrete-time domains, while admitting heterogeneous gains and deviations for the agents. Sufficient conditions for the stability of such systems, in both the domains, are presented in this paper along with the derivation of the reachable set, which is a set of points where the agents may converge asymptotically. The stability conditions are derived based on Gershgorins theorem. Simulations validating the theoretical results presented in this paper are provided.

Reachability of agents with double integrator dynamics in cyclic pursuit

Some recent work on cyclic pursuit systems with double integrator dynamics has probed the stability of certain proposed laws and investigated the stability of several formations for such a system of agents. Some of these laws use the relative position information of two leading neighbors, instead of one as in case of single integrator dynamics. In some others the relative position of only one leader is used along with its relative velocity and a damping term. In this paper, a new law is proposed which guarantees stability. An algorithm is proposed which enables rendezvous of the agents at any desired point in the two-dimensional space. The gains corresponding to each agent are different and, along with their initial velocities, are considered to be the decision variables. The theoretical results are backed by simulation studies.

Target Capturability Using Agents in Cyclic Pursuit

In the literature, several variants of the conventional cyclic pursuit law have been discussed. In this paper, one such variant, a modified heterogeneous cyclic pursuit scheme, has been proposed to capture a moving target. As a special case, when the target is stationary, the problem of capturing the target becomes the same as the rendezvous problem. The control laws proposed here ensure that such fixed targets (points) can always be collectively captured ( reached) and a maneuvering target can be captured, provided that the agents can rendezvous at its initial position. Agents with double-integrator dynamics have also been considered, and a suitable cyclic pursuit law has been proposed to ensure global reachability and target capturability for bounded target maneuver. The theoretical findings are backed by simulation results.

Boundary tracking using a hybrid cyclic pursuit scheme

There has been a lot of work in the literature, related to the mapping of boundaries of regions, using multiple agents. Most of these are based on optimization techniques or rely on potential fields to drive the agents towards the boundary and then retain them there while they space out evenly along the perimeter or surface (in two-dimensional and three-dimensional cases, respectively). In this paper an algorithm to track the boundary of a region in space is provided based on the cyclic pursuit scheme. This enables the agents to constantly move along the perimeter in a cluster, thereby tracking a dynamically changing boundary. The trajectories of the agents provide a sketch of the boundary. The use of multiple agents may facilitate minimization of tracking error by providing accurate estimates of points on the boundary, besides providing redundancy. Simulation results are provided to highlight the performance of the proposed scheme.

Generalized hierarchical cyclic pursuit

Cyclic pursuit has been an important connection topology in multi-agent systems. Many variants of the classical cyclic pursuit law have been analysed by researchers. Among these variants are homogeneous and heterogeneous cyclic pursuit, or single layer and hierarchical cyclic pursuit. In this paper hierarchical cyclic pursuit, with heterogeneous gains, has been considered. This paper generalizes existing results by allowing both heterogeneity in the gains, and extension of the single layer information flow graph to a multi-layer hierarchical structure. Some new results are presented about the reachability of agents in hierarchical cyclic pursuit. It is shown that the existing results may be obtained as special cases of the results obtained in this paper. Simulation results are provided to support the theoretical findings.

A Heterogeneous Cyclic Pursuit Based Strategy for Boundary Tracking

Abstract There has been a considerable amount of work done on tracking the boundaries of specified regions. The present paper focuses on the same problem. However, unlike previous works, this paper uses the cyclic pursuit scheme and its variants to locate the boundaries of specified regions, when the agents are initially deployed away from the region, and subsequently track the boundary continuously. The number of agents required under this paradigm is also considerably lesser than in existing strategies. In almost all cases, the algorithm described in this paper guarantees the convergence to the boundary. Simulation results have been presented to substantiate the efficacy of the proposed scheme.

Smith predictor based control strategies for nonminimum phase plants

The present paper proposes design strategies, based on the Smith predictor and its variants, for controlling nonminimum phase plants, by treating the right half plane (RHP) zeros of the system in the same way as the delay term in case of the conventional Smith predictor. Simple controllers, in conjunction with these Smith predictor like structures, can achieve good performance in terms of steady state error and disturbance rejection, for both type zero plants, as well as for plants with an integral mode. Additionally, here the order of the plant and the number of RHP zeros of the plant are not restricted. Simulations corroborate the theoretical results.

On existence of periodic solutions for stable interval plants with odd, sector type nonlinearities

In several systems, the physical parameters of the system vary over time or operating points. A popular way of representing such plants with structured or parametric uncertainties is by means of interval polynomials. However, ensuring the stability of such systems is a robust control problem. Fortunately, Kharitonovs theorem enables the analysis of such interval plants and also provides tools for design of robust controllers in such cases. The present paper considers one such case, where the interval plant is connected with a timeinvariant, static, odd, sector type nonlinearity in its feedback path. This paper provides necessary conditions for the existence of self sustaining periodic oscillations in such interval plants, and indicates a possible design algorithm to avoid such periodic solutions or limit cycles. The describing function technique is used to approximate the nonlinearity and subsequently arrive at the results. Furthermore, the value set approach, along with Mikhailov conditions, are resorted to in providing graphical techniques for the derivation of the conditions and subsequent design algorithm of the controller.

Zero miss distance guidance using feedforward and periodic control

There have been attempts at obtaining robust guidance laws to ensure zero miss distance (ZMD) for interceptors with parametric uncertainties. All these laws require the plant to be of minimum phase type to enable the overall guidance loop transfer function to satisfy strict positive realness (SPR). The SPR property implies absolute stability of the closed loop system, and has been shown in the literature to lead to ZMD because it avoids saturation of lateral acceleration. In these works higher order interceptors are reduced to lower order equivalent models for which control laws are designed to ensure ZMD. However, it has also been shown that when the original system with right half plane (RHP) zeros is considered, the resulting miss distances, using such strategies, can be quite high. In this paper, an alternative approach using the circle criterion establishes the conditions for absolute stability of the guidance loop and relaxes the conservative nature of some earlier results arising from assumption of in�nite engagement time. Further, a feedforward scheme in conjunction with a lead-lag compensator is used as one control strategy while a generalized sampled hold function is used as a second strategy, to shift the RHP transmission zeros, thereby achieving ZMD. It is observed that merely shifting the RHP zero(s) to the left half plane reduces miss distances signi�cantly even when no additional controllers are used to ensure SPR conditions.