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System stability is a fundamental concept in signal processing, often assessed using convolution. For a system to be considered bounded-input bounded-output (BIBO) stable, any bounded input signal must produce a bounded output signal. A bounded input signal is one where the modulus does not exceed a certain constant at any point in time.
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In structural engineering, the equilibrium of a system is not only determined by its equations of equilibrium but also with the help of constraints. Constraints refer to restrictions on the motion of a system. The proper combinations of constraints can minimize the total number of constraints needed to maintain a system in mechanical equilibrium. When this happens, the system is said to be statically determinate. For such systems, the unknown reaction supports can be estimated using equilibrium...
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The frequency-domain technique, commonly used in analyzing and designing feedback control systems, is effective for linear, time-invariant systems. However, it falls short when dealing with nonlinear, time-varying, and multiple-input multiple-output systems. The time-domain or state-space approach addresses these limitations by utilizing state variables to construct simultaneous, first-order differential equations, known as state equations, for an nth-order system.
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Summary
This summary is machine-generated.

This study addresses computing reachable sets with limited system knowledge. It proposes an underapproximation method for guaranteed reachable states, validated with an aircraft model.

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Area of Science:

  • Control Theory
  • Nonlinear Systems
  • Robotics

Background:

  • Computing reachable sets is crucial in nonlinear control.
  • Safety-critical online planning requires robust state estimation.
  • Limited knowledge of system dynamics poses a significant challenge.

Purpose of the Study:

  • To determine the set of states guaranteed to be reachable despite unknown system dynamics.
  • To develop a method for underapproximating this guaranteed reachable set.
  • To demonstrate the practical applicability of the proposed underapproximation.

Main Methods:

  • Underapproximation of the reachable set using a related known system.
  • Dynamics of the known system are based on velocity vectors consistent with assumed knowledge.
  • Validation through a case study involving a distressed aircraft model.

Main Results:

  • A method to underapproximate the guaranteed reachable set is presented.
  • The underapproximation is shown to be meaningful in practical scenarios.
  • The approach provides a conservative yet useful estimate of system reachability.

Conclusions:

  • The proposed underapproximation offers a viable solution for reachable set computation with limited dynamic information.
  • This method enhances safety in control systems where dynamics are not fully known.
  • The findings are relevant for online planning and control under uncertainty.