skip to main content


Title: Finite Sample Identification of Bilinear Dynamical Systems
Bilinear dynamical systems are ubiquitous in many different domains and they can also be used to approximate more general control-affine systems. This motivates the problem of learning bilinear systems from a single trajectory of the system’s states and inputs. Under a mild marginal meansquare stability assumption, we identify how much data is needed to estimate the unknown bilinear system up to a desired accuracy with high probability. Our sample complexity and statistical error rates are optimal in terms of the trajectory length, the dimensionality of the system and the input size. Our proof technique relies on an application of martingale small-ball condition. This enables us to correctly capture the properties of the problem, specifically our error rates do not deteriorate with increasing instability. Finally, we show that numerical experiments are well-aligned with our theoretical results.  more » « less
Award ID(s):
1931982
NSF-PAR ID:
10387218
Author(s) / Creator(s):
; ;
Date Published:
Journal Name:
Proceedings of the IEEE Conference on Decision Control
ISSN:
0743-1546
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. We address the problem of synthesizing a controller for nonlinear systems with reach-avoid requirements. Our controller consists of a reference controller and a tracking controller which drives the actual trajectory to follow the reference trajectory. We identify a type of reference trajectory such that the tracking error between the actual trajectory of the closed-loop system and the reference trajectory can be bounded. Moreover, such a bound on the tracking error is independent of the reference trajectory. Using such bounds on the tracking error, we propose a method that can find a reference trajectory by solving a satisfiability problem over linear constraints. Our overall algorithm guarantees that the resulting controller can make sure every trajectory from the initial set of the system satisfies the given reach-avoid requirement. We also implement our technique in a tool FACTEST. We show that FACTEST can find controllers for four vehicle models (3–6 dimensional state space and 2–4 dimensional input space) across eight scenarios (with up to 22 obstacles), all with running time at the sub-second range. 
    more » « less
  2. We develop an optimization-based framework for joint real-time trajectory planning and feedback control of feedback-linearizable systems. To achieve this goal, we define a target trajectory as the optimal solution of a time-varying optimization problem. In general, however, such trajectory may not be feasible due to , e.g., nonholonomic constraints. To solve this problem, we design a control law that generates feasible trajectories that asymptotically converge to the target trajectory. More precisely, for systems that are (dynamic) full-state linearizable, the proposed control law implicitly transforms the nonlinear system into an optimization algorithm of sufficiently high order. We prove global exponential convergence to the target trajectory for both the optimization algorithm and the original system. We illustrate the effectiveness of our proposed method on multi-target or multi-agent tracking problems with constraints. 
    more » « less
  3. M. Grimble (Ed.)
    Summary

    This paper presents the first model reference adaptive control system for nonlinear, time‐varying, hybrid dynamical plants affected by matched and parametric uncertainties, whose resetting events are unknown functions of time and the plant's state. In addition to a control law and an adaptive law, which resemble those of the classical model reference adaptive control framework for continuous‐time dynamical systems, the proposed framework allows imposing instantaneous variations in the reference model's trajectory to rapidly steer the trajectory tracking error to zero, while retaining the closed‐loop system's ability to follow a user‐defined signal. These results are enabled by the first extension of the classical LaSalle–Yoshizawa theorem to time‐varying hybrid dynamical systems, which is presented in this paper as well. A numerical simulation shows the key features of the proposed adaptive control system and highlights its ability to reduce both the control effort and the trajectory tracking error over a classical model reference adaptive control system applied to the same problem.

     
    more » « less
  4. Unmanned aerial vehicle (UAV) technology is a rapidly growing field with tremendous opportunities for research and applications. To achieve true autonomy for UAVs in the absence of remote control, external navigation aids like global navigation satellite systems and radar systems, a minimum energy trajectory planning that considers obstacle avoidance and stability control will be the key. Although this can be formulated as a constrained optimization problem, due to the complicated non-linear relationships between UAV trajectory and thrust control, it is almost impossible to be solved analytically. While deep reinforcement learning is known for its ability to provide model free optimization for complex system through learning, its state space, actions and reward functions must be designed carefully. This paper presents our vision of different layers of autonomy in a UAV system, and our effort in generating and tracking the trajectory both using deep reinforcement learning (DRL). The experimental results show that compared to conventional approaches, the learned trajectory will need 20% less control thrust and 18% less time to reach the target. Furthermore, using the control policy learning by DRL, the UAV will achieve 58.14% less position error and 21.77% less system power. 
    more » « less
  5. One of the primary research challenges in Attribute-Based Encryption (ABE) is constructing and proving cryptosystems that are adaptively secure. To date the main paradigm for achieving adaptive security in ABE is dual system encryption. However, almost all such solutions in bilinear groups rely on (variants of) either the subgroup decision problem over composite order groups or the decision linear assumption. Both of these assumptions are decisional rather than search assumptions and the target of the assumption is a source or bilinear group element. This is in contrast to earlier selectively secure ABE systems which can be proven secure from either the decisional or search Bilinear Diffie-Hellman assumption. In this work we make progress on closing this gap by giving a new ABE construction for the subset functionality and prove security under the Search Bilinear Diffie-Hellman assumption. We first provide a framework for proving adaptive security in Attribute-Based Encryption systems. We introduce a concept of ABE with deletable attributes where any party can take a ciphertext encrypted under the attribute string and modify it into a ciphertext encrypted under any string where is derived by replacing any bits of with symbols (i.e. ``deleting" attributes of ). The semantics of the system are that any private key for a circuit can be used to decrypt a ciphertext associated with if none of the input bits read by circuit are symbols and . We show a pathway for combining ABE with deletable attributes with constrained psuedorandom functions to obtain adaptively secure ABE building upon the recent work of Tsabary. Our new ABE system will be adaptively secure and be a ciphertext-policy ABE that supports the same functionality as the underlying constrained PRF as long as the PRF is ``deletion conforming". Here we also provide a simple constrained PRF construction that gives subset functionality. Our approach enables us to access a broader array of Attribute-Based Encryption schemes support deletion of attributes. For example, we show that both the Goyal~et al.~(GPSW) and Boyen ABE schemes can trivially handle a deletion operation. And, by using a hardcore bit variant of GPSW scheme we obtain an adaptively secure ABE scheme under the Search Bilinear Diffie-Hellman assumption in addition to pseudo random functions in NC1. This gives the first adaptively secure ABE from a search assumption as all prior work relied on decision assumptions over source group elements. 
    more » « less