Yingbo Zhao

On disturbance propagation in vehicle platoon control systems

This paper considers the problem of disturbance propagation in a vehicle platoon control system, where each vehicle has access to its position error relative to the preceding vehicle in the string. It is known that in such systems a small disturbance acting on one member can propagate downstream and cause large spacing errors between vehicles. A lower bound to the integral of the sensitivity function of the position errors with respect to a stochastic disturbance acting on the lead vehicle is presented. The tightness of the lower bound is discussed and numerical evaluations are provided to illustrate how this result can assist in practical controller design.

Scheduling of control nodes for improved network controllability

This paper considers the problem of controlling a linear time-invariant network by means of (possibly) time-varying set of control nodes. As control metric, we adopt the worst-case input energy to drive the network state from the origin to any point on the unit hypersphere in the state space. We provide a geometric interpretation of the controllability Gramian of networks with time-varying input matrices, and establish a connection between the controllability degree of a network and its eigenstructure. Based on the geometric structure of the controllability Gramian, we then propose a scheduling algorithm to select control nodes over time so as to improve the network controllability degree. Finally, we numerically show that, for a class of clustered networks, our algorithm improves upon the performance obtained by a constant set of control nodes, and outperforms an existing heuristic-based on column subset selection.

Disturbance propagation in strings of vehicles with limited leader information

This paper considers the problem of disturbance propagation in a string of vehicles, where each vehicle has access to the position error with respect to its preceding vehicle. In addition, the followers in the string may receive coded information sent by the leader over finite capacity side channels. A lower bound on the integral of the sensitivity function of the position errors with respect to a stochastic disturbance acting on the lead vehicle is presented. This bound depends on the open-loop unstable modes of the system, as in the classical Bode integral formula for single-input single-output systems. However, in this case, the bound also depends on the capacities of the side communication channels. Simulation results illustrating the tightness of the proposed bound are presented.

Gramian-Based Reachability Metrics for Bilinear Networks

This paper studies Gramian-based reachability metrics for bilinear control systems. In the context of complex networks, bilinear systems capture scenarios where an actuator not only can affect the state of a node but also interconnections among nodes. Under the assumption that the inputs infinity norm is bounded by some function of the network dynamic matrices, we derive a Gramian-based lower bound on the minimum input energy required to steer the state from the origin to any reachable target state. This result motivates our study of various objects associated with the reachability Gramian to quantify the ease of controllability of the bilinear network: the minimum eigenvalue (worst-case minimum input energy to reach a state), the trace (average minimum input energy to reach a state), and its determinant (volume of the ellipsoid containing the reachable states using control inputs with no more than unit energy). We establish an increasing returns property of the reachability Gramian as a function of the actuators, which, in turn, allows us to derive a general lower bound on the reachability metrics in terms of the aggregate contribution of the individual actuators. We conclude by examining the effect on the worst-case minimum input energy of the addition of bilinear inputs to difficult-to-control linear symmetric networks. We show that the bilinear networks resulting from the addition of either inputs at a finite number of interconnections or at all self loops with weight vanishing with the network scale remain difficult to control. Various examples illustrate our results.

Reachability metrics for bilinear complex networks

Controllability metrics based on the controllability Gramian have been widely used in linear control theory, and have recently seen renewed interests in the study of complex networks of dynamical systems. For example, the minimum eigenvalue and the trace of the Gramian are related to the worst-case and average minimum input energy, respectively, to steer the state from the origin to a target state. This paper explores similar questions that remain unanswered for bilinear control systems. In the context of complex networks, bilinear systems characterize scenarios where an actuator not only can affect the state of a node, but also can affect the strength of the interconnections among some neighboring nodes. Under the assumption that the infinity norm of the input is bounded by some function of the network dynamic matrices, we derive a lower bound on the minimum input energy to steer the state of a bilinear network from the origin to any reachable target state based on the generalized reachability Gramian of bilinear systems. We also provide a lower bound on the average minimum input energy over all target states on the unit hypersphere in the state space. Based on the reachability metrics proposed, we propose an actuator selection method that provides guaranteed minimum average input energy.

Feedback Stabilization of Bernoulli Jump Nonlinear Systems: A Passivity-Based Approach

We study feedback stabilization of a Bernoulli jump nonlinear system. First, the relationship between stochastic passivity and stochastic stability is established. A state feedback controller that stabilizes a wide class of Bernoulli jump nonlinear systems is then designed using passivity-based tools. The advantage of our approach is that the nonlinear dynamics can be non-affine in the control input.

Disturbance propagation analysis in vehicle formations: An information-theoretic approach

We consider the problem of disturbance propagation in a control system where a group of vehicles aims to move in a formation with a tree topology. The control law at every vehicle depends on its position error with respect to its parent vehicle in the tree as well as on coded information transmitted by other vehicles across side communication channels. A lower bound on the integral of the log sensitivity function of the position errors for any vehicle with respect to a stochastic disturbance acting on the lead vehicle is presented. The effect of the side information channels is illustrated through some examples. It is also shown that in some cases the lower bound is achievable through appropriate design of the controllers and encoder/decoder pairs.

Feedback Passivation of Discrete-Time Systems Under Communication Constraints

Passivity is a desirable property of a dynamical system because it implies stability and is invariant under negative feedback and parallel interconnections. Feedback passivation is the process of making a nonpassive system passive through feedback control. In this technical note, we study the problem of feedback passivation when the controller has limited information about the state of the plant. Nonlinear plants that are linear in the control inputs are considered. The main result of the technical note is a certainty equivalence principle: any state feedback controller that ensures closed-loop input-strict passivity with index μ using the exact state of the plant will also ensure closed-loop stochastic quasi passivity using an estimate of the state, provided that the infinity norm of the estimation error process is bounded by some function of μ. A corollary is that for linear systems, although passivity is more strict than stability, feedback passivation does not place more constraints on the estimation error and hence does not demand more from the communication channel than mean square stabilization.

A Bode-Like Integral for Discrete Linear Time-Periodic Systems

We present a generalization of the Bode integral formula for discrete-time linear periodic systems. It is shown that similar to the classical Bode integral formula, the sensitivity integral for a discrete-time linear periodic system depends only on the open-loop dynamics of the system; in particular, on the open-loop characteristic multipliers outside the unit circle in the complex plane. The integral is derived by using an asymptotic eigenvalue distribution theorem for block Toeplitz matrices, which does not require the open loop system to be stable or the disturbance to be Gaussian. The result is demonstrated through application to a class of multi-rate sampled data systems with commensurate rates.

Identification of linear networks with latent nodes

We study identification of linear networks under the assumption that only a subset of all the nodes in the network can be observed. The observable nodes are called manifest nodes and they form the manifest subnetwork. The unobservable nodes are called latent nodes and the number of latent nodes is unknown. We explore the possibility of identifying the transfer function of the manifest subnetwork and whether an interaction between two manifest nodes is direct or mediated by latent nodes. In particular, we show that if the external inputs are injected into a linear network only through the manifest nodes, then there exists an auto-regressive model whose transfer function is arbitrarily close to the transfer function of the manifest subnetwork in the H∞ norm sense. Moreover, we prove that the least-squares method provides consistent estimate of the auto-regressive model using the measured states of the observed nodes. Finally, we show that if the latent subnetwork is acyclic, then the transfer function of the manifest subnetwork can be perfectly identified using the least-squares auto-regressive method. Various examples illustrate our results.