A trajectory‐based method for constructing null controllable regions

Homer, Tyler; Mahmood, Maaz; Mhaskar, Prashant

doi:10.1002/rnc.4805

Cited by 13 publications

(7 citation statements)

References 23 publications

(55 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…A set is said to be control invariant if trajectories that start from it, can be forced to remain in it by using admissible control inputs. It is worth mentioning that control invariant sets are closely linked to viability theory [4,5], reachability analysis [6,7] and null controllability [8,9,10]. Unfortunately, determining control invariant sets is a very challenging task, even for linear systems.…”

Section: Introductionmentioning

confidence: 99%

An efficient implementation of graph-based invariant set algorithm for constrained nonlinear dynamical systems

Decardi-Nelsona¹,

Liu²

2022

Preprint

View full text Add to dashboard Cite

The graph-based invariant set (GIS) algorithm is a promising set-based technique for computing the largest (with respect to inclusion) control invariant set of general discrete-time nonlinear dynamical systems. However, like other invariant set algorithms for nonlinear systems, the GIS algorithm may require a lot of resources when computing the control invariant set. This limits its applicability to higher dimensional systems. In this work, we present an improved and efficient implementation of the GIS algorithm for general discrete-time controlled nonlinear systems. We first identify the bottlenecks through extensive analysis, and then provide remedial procedures to improve the implementation of the GIS algorithm. Specifically, we developed an adaptive subdivision scheme using a supervised machine learning-based algorithm to reduce the cell growth rate and parallelize the graph construction step. We extensively demonstrate the performance of the improved GIS algorithm using a numerical example and compare the result to that of the standard GIS algorithm. The results show that the adaptive subdivision and the parallelization improved the speed of the algorithm by about 8x and 3x respectively, that of the standard GIS algorithm.

show abstract

Section: Introductionmentioning

confidence: 99%

An efficient implementation of graph-based invariant set algorithm for constrained nonlinear dynamical systems

Decardi-Nelsona¹,

Liu²

2022

Preprint

View full text Add to dashboard Cite

show abstract

“…6,7 However, the formal development of stabilization using CCLFs for nonlinear systems along with explicit control design is still lacking. More recently, the work in Reference [8] presented some computational techniques for NCR construction. This work utilizes a simulation-based approach resulting in high computational cost both for NCR construction and utilization in the control design.…”

Section: Introductionmentioning

confidence: 99%

Controllability minimum principle based construction of the null controllable region for nonlinear systems

Mahmood

Homer

Mhaskar

2021

Intl J Robust & Nonlinear

Self Cite

View full text Add to dashboard Cite

The present manuscript addresses the problem of designing a procedure for constructing the null controllable Region (the set of states from where stabilization is achievable subject to constraints). To this end, a controllability minimum principle based computationally tractable approach for constructing the null controllable region is presented. Simulation results are used to illustrate the computation of the NCR for several examples.

show abstract

“…In comparison with linear systems, much less research exists on the null controllable regions of nonlinear systems. A method was presented by Homer et al for the control of input-constrained nonlinear systems that provided guaranteed stabilization in the entire null controllable region [40], [41]. Nonlinear systems are more difficult to study and require more attention [42], [43].…”

Section: Introductionmentioning

confidence: 99%

A Study on Stability Boundary of Highly Flexible Aircraft With Saturation Constraint

Cao

Liu

et al. 2021

IEEE Access

View full text Add to dashboard Cite

This paper deals with investigating the closed-loop stability boundary of the highly flexible aircraft with structural flexibility and input saturation constraint. A method is presented to analyze the stable region based on the system features of the open-loop instability. In this paper, a dynamic model of highly flexible aircraft is made and the dynamic characteristics are analyzed and the long period mode and stability are investigated in terms of the trimmed model. Considering the saturation constraint of elevator deflection, the closed-loop stability boundary of the system under saturation constraint is discussed by combining the open-loop instability features of highly flexible aircraft. The analysis indicates that the boundary is related to the left eigenvector consistent with the amplitude constraint and the unstable poles of the control signals. Based on the long period instability of the aircraft, the formula of closed-loop stability boundary is analytically obtained. The convergence region of highly flexible aircraft is verified in terms of the LQR controller. The influence of structural flexibility and saturation constraint amplitude of elevator on the stability boundary of highly flexible aircraft is analyzed based on state constraints, which is also compared with the rigid aircraft. The simulation results show that the closed-loop stability of the system is restricted by the open-loop characteristic of the system and the control input saturation constraint.

show abstract

A trajectory‐based method for constructing null controllable regions

Cited by 13 publications

References 23 publications

An efficient implementation of graph-based invariant set algorithm for constrained nonlinear dynamical systems

An efficient implementation of graph-based invariant set algorithm for constrained nonlinear dynamical systems

Controllability minimum principle based construction of the null controllable region for nonlinear systems

A Study on Stability Boundary of Highly Flexible Aircraft With Saturation Constraint

Contact Info

Product

Resources

About