CAD.3 - Construct a Jointly Admissible Command Domain
CAD.3 - Construct a Jointly Admissible Command Domain Type: Method pattern Status: Stable…
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CAD.3 - Construct a Jointly Admissible Command Domain Type: Method pattern Status: Stable…
In CAD.3 - Construct a Jointly Admissible Command Domain
For the linear interface of CAD.2, write Choose a proposed command set S of pairs (z,v), a bounded mismatch set W, and an error set E containing the admitted initial error. A sufficient one-step condition is Here \oplus is addition of sets. This is a property…
In CAD.3 - Construct a Jointly Admissible Command Domain
The designer obtains commands that the whole architecture can support under stated conditions, or a precise reason to revise it. Some planning freedom is exchanged for dependable correction. The result may be conservative and computationally expensive; those…
In CAD.3 - Construct a Jointly Admissible Command Domain
CAD.3:6 - Bias-Annotation Robust envelopes can be unnecessarily restrictive, especially when correlations are discarded. Conversely, nominal examples can make the operating domain look larger than the evidence warrants. Keep sufficiency, necessity,…
In CAD.3 - Construct a Jointly Admissible Command Domain
CAD.3:10 - Architectural Rationale The lower guarantee and upper assumption concern the same connected behavior. Error propagation and constraint propagation therefore form one coupled construction. Adding continuation prevents a one-step solution from being…
In CAD.3 - Construct a Jointly Admissible Command Domain
CAD.3:3 - Forces Force Consequential tension Planning freedom and correction authority Aggressive nominal commands consume input needed for error rejection. Tight bounds and defensible bounds A smaller assumed error enlarges the command domain but can…
In CAD.3 - Construct a Jointly Admissible Command Domain
CAD.3:2 - Problem The layers can make mutually inconsistent promises. The tracker guarantees a small error only for modest commands, while the planner assumes that error before restricting its commands. Tightening an upper constraint by an arbitrary tolerance…
In CAD.3 - Construct a Jointly Admissible Command Domain
CAD.2 supplies the exact connected dynamics. CAD.1 is the return when no useful command domain exists for the selected split. CAD.4 uses the size and cost of the feasible domain in whole-candidate comparison. MMP.18 supplies general compatibility reasoning;…
In CAD.3 - Construct a Jointly Admissible Command Domain
… from CAD.2 and one limiting constraint. Derive the deviation that consumes its margin. The first useful result is a command domain with an invariant error bound and an admissible continuation, or a specific failure that returns the design for revision. A…
In CAD.3 - Construct a Jointly Admissible Command Domain
CAD.3:7 - Conformance Checklist The bound covers the actual initial condition, command class, mismatch and timing modes. Switching uses a common invariant set or proved transitions between the admitted mode or phase sets. A continuous-time claim ends at the…
In CAD.3 - Construct a Jointly Admissible Command Domain
CAD.3:8 - Common Anti-Patterns and How to Avoid Them A tolerance selected first and justified afterward can consume imaginary authority; derive it with the command domain. A nonempty feasible set can contain dead ends; test successors. A sampled safe plan is…
In CAD.3 - Construct a Jointly Admissible Command Domain
For the held-reference case of CAD.2, a=1/2,N=4,\delta=0.1 give E=8/75. Since |u|=(1-a)|e|, a sufficient input bound is 4/75\approx0.05333<0.06. Requiring |r|\leq1-E=67/75 also suffices for |x|\leq1. This position tightening is conservative: the scalar convex…
In CAD.3 - Construct a Jointly Admissible Command Domain
CAD.3:4.6 - Separate recognition, mathematical assurance and physical reliance A shrinking error trace or plausible margin recognizes a promising design. The invariance and continuation arguments establish conditional properties of a mathematical model. Model…
In CAD.3 - Construct a Jointly Admissible Command Domain
… The price is a sufficient domain that may exclude useful commands. A serious alternative for a fixed qualified loop is a governor's joint state-command admissible set (CAD.Reference:4.5.1). It can retain relations discarded by one common error envelope.…
In CAD.3 - Construct a Jointly Admissible Command Domain
With x=Pz+e and u=Qz+Rv+Ke, require These constraints reserve physical room and actuator authority for correction. For an output constraint use the actual output map, including the mismatch term in CAD.2:4.1. For example, if X=\{x:Lx\leq b\} and E is the…