Andrés A. Peters

Leader tracking in homogeneous vehicle platoons with broadcast delays

For vehicle platoons, the leader following control architecture is known to be capable of achieving string stability while maintaining tight formations. In this paper, we study a variety of schemes where the leader state is available to the other members of the platoon. We show that in some cases it is possible to achieve string stability in the presence of certain amounts of time delay in the leader state reception. We also compare other properties of the different schemes and discuss some of their advantages and disadvantages.

Performance bounds in linear control of unstable MIMO systems with pole location constraint

This paper proposes a methodology to compute quadratic performance bounds when the closed loop poles of a discrete-time multivariable control loop are confined to a disk, centred at the origin, and with radius less than one. The underlying philosophy in this constraint is to avoid certain undesirable dynamic features which arise in quadratic optimal designs. An expression for the performance loss due to the pole location constraint is also provided. Using numerical examples, we show that the performance loss is compensated by an improved transient performance, specially visible in the control signals.

Leader velocity tracking and string stability in homogeneous vehicle formations with a constant spacing policy

For vehicle platoons, the leader following control structure is well known for being capable of achieving string stability. In this paper, the linear string case is modified so that each follower tracks the instantaneous velocity of the leader in addition to the position of its predecessor. We show that it is possible to achieve string stability, under some basic assumptions, with this approach. We also discuss some of the benefits of the use of this method such as lowered coordination requirements and simplified communication needs.

On the Error Estimates for the Finite Element Approximation of a Class of Boundary Optimal Control Systems

In this article, we consider an application of the abstract error estimate for a class of optimal control systems described by a linear partial differential equation (as stated in Numer. Funct. Anal. Optim. 2009; 30:523–547). The control is applied at the boundary and we consider both, Neumann and Dirichlet optimal control problems. Finite element methods are proposed to approximate the optimal control considering an approximation of the variational inequality resulting from the optimality conditions; this approach is known as classical one. We obtain optimal order error estimates for the control variable and numerical examples, taken from the literature, are included to illustrate the results.

Performance Bounds in

This note deals with performance bounds for the H infin-optimal control of discrete-time LTI plants. The case studied corresponds to stable scalar plants with arbitrary relative degree but no finite non-minimum phase zero. By using Neharis Theorem and a reformulation of the standard Youla Parameterization a closed-form expression for the characteristic polynomial of the associated eigenvalue problem is obtained. Also, we derive an analytic expression for the optimal H infin cost as a function of the plant relative degree.

{\cal H}_{\infty}

In this paper, we study a formation control scheme for a 1-D string of vehicles. Each member tracks the movement of its immediate predecessor but also the first vehicle tracks the position of the last member of the string. We discuss conditions for the stability of the full interconnected system and show that if a constant spacing policy is used, the stability of the system is lost after the string size exceeds a certain number depending on the model parameters (vehicles and controllers). Additionally, we study the use of a constant time headway spacing policy. If the associated time headway parameter is greater than a critical value, the interconnected system is stable and string stable for any string size. Finally, we show that if an independent leader vehicle is added to the formation and every follower has access to this leader position, the cyclic formation with a constant spacing policy can be made stable and string stable by appropriately selecting a design parameter.

Optimal Control for Stable SISO Plants With Arbitrary Relative Degree

In this paper, we study a formation control scheme that achieves a tight formation in a 1D platoon. The scheme achieves constant inter-vehicle spacings (with no transient) for almost every vehicle pair whenever there are no disturbances. We build up from the basic leader following approach with a modification in the weight selection. In particular, each member tracks the movement of its immediate predecessor but also uses the leader state, which needs to be transmitted, in order to achieve a tight formation. The key design choice is the use of filters for the measurements that set the transfer functions from the leader trajectory to the inter-vehicle spacings to zero whenever possible. We support the analysis of the architecture with numerical simulations.

Cyclic interconnection for formation control of 1-D vehicle strings

In this paper, we study a formation control scheme for a 1D string of vehicles. Each member tracks the movement of its immediate predecessor but also the first vehicle tracks the position of the last member of the string. We discuss conditions for the stability of the full interconnected system and show that if a constant inter-vehicle spacing policy is used, the interconnection becomes unstable after the string size surpasses a critical value. Moreover, we show that if constant time headway is used in the spacing policy, stability can be recovered for any string size. String stability is also achieved as a consequence.