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This brief is concerned with the formation control problem of a multi-agent system composed of multiple quadrotors tasked to achieve aggressive trajectory tracking with prescribed formation patterns. An underactuated model with six degrees of freedom is considered for each quadrotor, the dynamics of which account for nonlinearities, parameter uncertainties, and external disturbances. A robust control approach is proposed that stems from linear quadratic regulation and robust compensation theory fundamentals. Theoretical analysis and simulation results validate the effectiveness of the presented theoretical framework.

In this paper, connections between the control allocation and linear quadratic (LQ) control frameworks for optimally distributing control inputs in weakly input redundant systems are explored. It is also shown that, for a representative class of exogenous disturbance and reference signals, the LQ control technique is identical to the so-called optimal control subspace-based (OCS) control allocation technique. However, for this equivalence to hold, the OCS control allocation technique requires evaluation of a (generally) non-causal relationship between control inputs, while the LQ control technique requires perfect knowledge of the system, disturbance and reference states. In practice, neither of these conditions is achievable; therefore, approximations are needed. In this regard, the OCS control allocation technique is superior because it is explicit about the relationship that must be accurately approximated to attain optimality; this enables good approximations of the optimal relationship to be realized. Conversely, the LQ control technique implicitly approximates the optimal relationship via estimation of states, disturbances and/or reference signals. In a comparison with a classical example based on the Kalman filter, the OCS control allocation is shown to be superior in preserving the optimal alignment of redundant control inputs, thus introducing enhanced performance with reduced cost.

It is well known that decentralized linear time-invariant controllers fail to stabilize interconnected systems with unstable decentralized fixed modes. This paper employs a high-frequency ( ω ), continuous-time, linear periodic controller to solve this problem. In addition to handling a general class of strongly connected systems, the proposed controller ensures negligible ripples ( O ( 1 / ω ) at most) in the plant output, unlike O ( 1 ) ripples with the existing ones. An H ∞ -loop-transfer-recovery based sequential method is used to design the controller in such a way that it achieves some centralized linear quadratic performance along with some desired loop properties in averaged sense. The results are illustrated using a suitable example.

This paper presents a reduction technique for the continuous-time constrained generalized Riccati equation arising in the context of the singular Linear Quadratic (LQ) optimal control problem. This technique allows to express the solutions of the constrained generalized Riccati equation in terms of the solutions of a reduced-order standard Riccati equation. This result is used to provide a solution to the singular LQ problem with closed-loop stability in the case when the allowed controls are restricted to be regular for any initial condition.

In this paper, we consider infinite horizon linear-quadratic Stackelberg games for a discrete-time stochastic system with multiple decision makers. Necessary conditions for the existence of the Stackelberg strategy set are derived in terms of the solvability of cross-coupled stochastic algebraic equations (CSAEs). As an important application, the hierarchical H ∞ -constraint control problem for the infinite horizon discrete-time stochastic system with multiple channel inputs is solved using the Stackelberg game approach. Computational methods for solving the CSAEs are also discussed. A numerical example is provided to demonstrate the usefulness of the proposed algorithms.

This paper is concerned with general mean-field (MF) linear-quadratic (LQ) games of stochastic large-population system, where the individual diffusion coefficient can depend on both the state and the control of the agent. Moreover, the control weight in the cost functional could be indefinite. The asymptotic suboptimality property (namely, ϵ-Nash equilibrium) of the decentralized strategies for the LQ games is derived through the consistency condition. The impact of the population’s collective behaviors and the consistency of the mean field estimation are illustrated by the numerical results. A pricing problem is also studied, for which the decentralized suboptimal price is obtained.

This paper addresses the discrete-time finite-horizon linear quadratic (LQ) optimal control problem in the case in which the quadratic forms in the performance index are not assumed to be positive semidefinite, but only symmetric. We provide a necessary and sufficient condition for the existence of an optimal control.

Self-triggered control is a recently proposed paradigm that abandons the more traditional periodic time-triggered execution of control tasks with the objective of reducing the utilization of communication resources, while still guaranteeing desirable closed-loop behavior. In this paper, we introduce a self-triggered strategy based on performance levels described by a quadratic discounted cost. The classical LQR problem can be recovered as an important special case of the proposed self-triggered strategy. The self-triggered strategy proposed in this paper possesses three important features. Firstly, the control laws and triggering mechanisms are synthesized so that a priori chosen performance levels are guaranteed by design. Secondly, they realize significant reductions in the usage of communication resources. Thirdly, we address the co-design problem of jointly designing the feedback law and the triggering condition. By means of a numerical example, we show the effectiveness of the presented strategy. In particular, for the self-triggered LQR strategy, we show quantitatively that the proposed scheme can outperform conventional periodic time-triggered solutions. Keywords : Self-triggered control; Networked control systems; Linear quadratic regulator; Limiting control actions; LQG control

In Buckdahn, Djehiche, Li, and Peng (2009), the authors obtained mean-field Backward Stochastic Differential Equations (BSDEs) in a natural way as a limit of some highly dimensional system of forward and backward SDEs, corresponding to a great number of ''particles'' (or ''agents''). The objective of the present paper is to deepen the investigation of such mean-field BSDEs by studying their stochastic maximum principle. This paper studies the stochastic maximum principle (SMP) for mean-field controls, which is different from the classical ones. This paper deduces an SMP in integral form, and it also gets, under additional assumptions, necessary conditions as well as sufficient conditions for the optimality of a control. As an application, this paper studies a linear quadratic stochastic control problem of mean-field type.

In this paper, we consider the non-cooperative linear feedback Nash quadratic differential game with an infinite planning horizon for descriptor systems of index one. The performance function is assumed to be indefinite. We derive both necessary and sufficient conditions under which this game has a Nash equilibrium.

In this note we consider the static output feedback linear quadratic control problem. We present both necessary and sufficient conditions under which this problem has a solution in case the involved cost depends only on the output and control variables. This result is used to present both necessary and sufficient conditions under which the corresponding linear quadratic differential game has a Nash equilibrium in case the players use static output feedback control. Another consequence of this result is that the conditions also provide sufficient conditions for the static output stabilizability problem. Of course, in case these conditions are not met this does not mean that the system is not stabilizable via static output feedback.

In this paper, a strategy based on the linear quadratic design, which progressively accommodates the feedback control law, is proposed. It significantly reduces the loss of performance that results from the time delay needed by fault accommodation algorithms to provide a solution. An aircraft example is given to illustrate the efficiency of progressive accommodation.

A method for bumpless transfer using ideas from LQ theory is presented and shown to reduce to the Hanus conditioning scheme under certain conditions.

A model-free approach to linear quadratic (LQ) performance assessment is presented in this paper. First a test for LQ optimality, based on closed-loop signals, is presented. Its result indicates whether the controller should be adjusted. From the same test it is possible to determine the closed-loop pole positions which would be obtained by using the LQ optimal controller. These may then be used in a direct adaptive control scheme to adjust the controller. Both state and output feedback are addressed for discrete-time, single-input-single-output (SISO), linear, time-invariant processes.

In this paper, the authors aim at designing a partial state reference model adaptive controller for multivariable systems. The partial state reference model concept is particularly used to incorporate an appropriate tracking capability into the linear quadratic control design. Simulation studies, involving a binary distillation column model, are carried out to emphasize the performances of the proposed adaptive controller.

In this paper we announce a new rigorous 'state space' formulation for systems with delays in state and control variables. This is used to solve the linear-quadratic optimal control problem over both finite and infinite time horizons. In each case abstract operational Riccati equations are derived to characterize the feedback gains. This paper extends recent results of Vinter and Kwong.

Certain frequency-shaped standard linear quadratic (LQ) controllers involving state feedback have attractive loop robustness properties. These robustness properties may vanish in passing to an output feedback scheme, as when state estimates are used instead of states. The known exception to date is when the plants are minimum phase and state estimation with loop recovery is used, as in LQG/LTR designs. In this paper, generalized frequency-shaped LQ theory is developed for plants with matrix fraction descriptions. For the case of minimum phase plants, a spectral factorization based construction procedure is given which leads to stable output feedback controllers that are optimal in an LQ sense. Among the class of such optimal LQ controllers, these achieve the attractive loop robustness properties of standard LQ state feedback designs (and of LQG/LTR output feedback designs). Perhaps surprisingly the controllers can be expressed in terms of the solution of a transfer function matrix Riccati equation. The LQ/Riccati theory of the paper specializes to known theory in the case when the plant outputs are the states and the indices are not frequency shaped.

A new procedure for constrained pole-placement is presented. The poles of the closed loop system are placed within a circle in the left half plane. The design procedure is noniterative and the solution is obtained via linear quadratic (LQ) design for a transformed system. The circle can be chosen in order to obtain good transient properties of the closed loop system. The method combines the properties of pole-placement and LQ-design.

This paper provides a method for designing 'optimal' decentralized controls for linear time-invariant interconnected systems. The optimality is with respect to a quadratic cost criterion. An algorithm is proposed which uses the method of feasible directions and provides a local minimum while ensuring, at each iteration, the stability of the overall system.

This paper proposes a cost effective control law for a linear time invariant (LTI) system having an extra set of exogenous inputs (or external disturbances) besides the traditional set of control inputs. No assumption is made with regard to a priori knowledge of the modeling equations for the exogenous inputs. The problem of optimal control for such a system is defined in the standard framework of linear quadratic control and an extended linear quadratic regulator (ELQR) is proposed as the solution to the problem. The ELQR approach is demonstrated through an example and is shown to be significantly more cost effective than currently available approaches for linear quadratic control.