his paper develops the fundamentals of optimaltuning periodic-gain fractional delayed state feedback control for a class of linear fractional order periodic time-delayed systems.his paper develops the fundamentals of optimal-tuning periodic-gain fractional delayed state feedback control for a class of linear fractional order periodic time-delayed systems.T Although there exist techniques for the state feedback control of linear periodic timedelayed systems by discretization of the monodromy operator, there is no systematic method to design state feedback control for linear fractional periodic time-delayed (FPTD) systems. This paper is devoted to defining and approximating the monodromy operator for steady state solution of FPTD systems. It is shown that the monodromy operator cannot be achieved in a close form for FPTD systems, and hence the short memory principle along with the fractional Chebyshev collocation (FCC) method are used to approximate the monodromy operator. The proposed method guarantees a near-optimal solution for FPTD systems with fractional orders close to unity. The proposed technique is illustrated in examples, specifically in finding optimal linear periodic-gain fractional delayed state feedback control laws for the fractional damped Mathieu equation and a double inverted pendulum subjected to a periodic retarded follower force with fractional dampers in which it is demonstrated that the use of time-periodic control gains in the fractional feedback control generally leads to a faster response.

This paper presents a technique to obtain the transition curves of fractional periodic time-delayed (FPTD) systems based on a proposed explicit harmonic balance (EHB) method. This method gives the analytical Hill matrix of FPTD systems explicitly with a symbolic computation-free algorithm. Furthermore, all linear operations on Fourier basis vectors including fractional order derivative operators and time-delayed operators for a linear FPTD system are obtained. This technique is illustrated with parametrically excited simple and double pendulum systems, with both time-delayed states and fractional damping.

In this paper, an SE(3)-constrained extended Kalman filter is proposed in continuous time as well as in a more practical continuous-discrete framework. The filter allows for the state estimation of the 6-DOF rigid body motion while accounting for measurement error statistics and using the rotation matrix instead of an quaternions or other attitude parameterizations. The proposed filter differs from the recently proposed SO(3)-constrained attitude filter in that only a subset of the configuration states are constrained in the present filter. Its effectiveness is demonstrated in a numerical example in which its performance is compared with that of an existing SE(3) estimator from the literature and a Monte Carlo simulation is out carried out to provide credence to the accuracy of the proposed filter.

The contribution of this paper is a control synthesis and stability verification framework for linear time-invariant multiagent systems with heterogeneous actuator dynamics and system uncertainties. In particular, we first propose a distributed adaptive control architecture in a leader-follower setting for this class of high-order multiagent systems. The proposed architecture uses a hedging method, which alters the ideal reference model dynamics of each agent in order to ensure correct adaptation in the presence of heterogeneous actuator dynamics of these agents. We then use Lyapunov stability theory and linear matrix inequalities to analyse the proposed architecture. This analysis reveals a stability condition, where evaluation of this condition with respect to a given graph topology allows stability verification of the controlled multiagent system. From a practical point of view, this condition also shows a fundamental tradeoff between heterogeneous agent actuation capabilities and unknown parameters in agent dynamics. Several illustrative numerical examples are also provided to demonstrate the efficacy of the proposed architecture.