Optimal Control of Vehicular Formations With Nearest Neighbor Interactions

Abstract

We consider the design of optimal localized feedback gains for one-dimensional formations in which vehicles only use information from their immediate neighbors. The control objective is to enhance coherence of the formation by making it behave like a rigid lattice. For the single-integrator model with symmetric gains, we establish convexity, implying that the globally optimal controller can be computed efficiently. We also identify a class of convex problems for double-integrators by restricting the controller to symmetric position and uniform diagonal velocity gains. To obtain the optimal non-symmetric gains for both the single-and the double-integrator models, we solve a parameterized family of optimal control problems ranging from an easily solvable problem to the problem of interest as the underlying parameter increases. When this parameter is kept small, we employ perturbation analysis to decouple the matrix equations that result from the optimality conditions, thereby rendering the unique optimal feedback gain. This solution is used to initialize a homotopy-based Newton's method to find the optimal localized gain. To investigate the performance of localized controllers, we examine how the coherence of largescale stochastically forced formations scales with the number of vehicles. We establish several explicit scaling relationships and show that the best performance is achieved by a localized controller that is both non-symmetric and spatially-varying.

Submodularity in Dynamics and Control of Networked Systems

“…For a leader-follower system with additive link noise, the steady-state error due to noise was shown to be proportional to the graph effective resistance between the leader and follower agents in [12]. In [83], decentralized control for vehicular networks with static topology, single-and double-integrator dynamics, and noise in the agent states was considered, and it was proved that at least one leader node must be present in the network to achieve stability. In [10], existing schemes for consensus and vehicle formation control were studied in the H 2 -norm framework.…”

“…When state updates that are broadcast by a node are corrupted by noise at the receiver, the receiving node will update its state based on incorrect information, causing state errors that propagate through the network. The choice of leader nodes determines the level of error in the follower node states due to the propagation of leader inputs through noisy communication links [83,108].…”

Static LQG teams with countably infinite players

“…In a recent tutorial paper [12], we highlighted some of the differences between these two approaches. Relevant to our paper are the recent results on frequency domain characterization of solutions to deterministic teams, as well as quadratic stochastic dynamic teams under the a priori restriction to linear policies [13], [14], [15], [16], [17].…”

Optimal Distributed Control for Platooning via Sparse Coprime Factorizations

“…In [9] optimal quadratic regulators for platooning are proposed while showing that for an increasing number of vehicles the resulted LQR problems become ill-posed. It was later proved in [11] that "local" measurements based distributed controllers cannot achieve "coherent" coordination in large-sized platoons, results further extended in [10] as to achieve superior coherence formation via optimal controllers.…”

“…Since no available control solution was deemed completely satisfactory, considerable research efforts are still being spent [9], [10], [12], [31], [21] motivated by the advent of assisted driving systems and the imminence of driverless vehicles.…”