Package tulip :: Package abstract :: Module discretization :: Class AbstractPwa

Class AbstractPwa

Discrete abstraction of PWA dynamics, with attributes:

ppp: Partition into Regions. Each Region corresponds to a discrete state of the abstraction
type: PropPreservingPartition
ts: Finite transition system abstracting the continuous system. Each state corresponds to a Region in ppp.regions. It can be fed into discrete synthesis algorithms.
type: FTS
ppp2ts: bijection between ppp.regions and ts.states. Has common indices with ppp.regions. Elements are states in ts.states. (usually each state is a str)
type: list of states
pwa: system dynamics
type: PwaSysDyn
pwa_ppp: partition preserving both:
- propositions and
- domains of PWA subsystems
Used for non-conservative planning. If just LtiSysDyn, then the only difference of pwa_ppp from orig_ppp is convexification.

type: PropPreservingPartition
orig_ppp: partition preserving only propositions i.e., agnostic of dynamics
type: PropPreservingPartition
disc_params: parameters used in discretization that should be passed to the controller refinement to ensure consistency
type: dict

If any of the above is not given, then it is initialized to None.

Notes

There could be some redundancy in ppp and ofts, in that they are both decorated with propositions. This might be useful to keep each of them as functional units on their own (possible to change later).
The 'Pwa' in AbstractPwa includes LtiSysDyn as a special case.

Instance Methods

__init__(self, ppp=None, ts=None, ppp2ts=None, pwa=None, pwa_ppp=None, ppp2pwa=None, ppp2sys=None, orig_ppp=None, ppp2orig=None, disc_params=None)
x.__init__(...) initializes x; see help(type(x)) for signature

__str__(self)
str(x)

ts2ppp(self, state)

ppp2trans(self, region_index)
Return the transition set constraint and active subsystem,

(i, pwa.pwa_ppp[i])

ppp2pwa(self, region_index)
Return dynamics and predicate-preserving region and its index for PWA subsystem active in given region.

(i, pwa.list_subsys[i])

ppp2sys(self, region_index)
Return index and PWA subsystem active in indexed region.

(i, orig_ppp.regions[i])

ppp2orig(self, region_index)
Return index and region of original partition.

_debug_str_(self)

plot(self, show_ts=False, only_adjacent=False, color_seed=None)
Plot partition and optionally feasible transitions.

verify_transitions(self)

Inherited from object: __delattr__, __format__, __getattribute__, __hash__, __new__, __reduce__, __reduce_ex__, __repr__, __setattr__, __sizeof__, __subclasshook__

Properties
Inherited from `object`: `__class__`

Method Details

init(self, ppp=None, ts=None, ppp2ts=None, pwa=None, pwa_ppp=None, ppp2pwa=None, ppp2sys=None, orig_ppp=None, ppp2orig=None, disc_params=None)
(Constructor)

x.__init__(...) initializes x; see help(type(x)) for signature

Overrides: object.__init__: (inherited documentation)

str(self)
(Informal representation operator)

str(x)

Overrides: object.__str__: (inherited documentation)

ppp2trans(self, region_index)

Return the transition set constraint and active subsystem,

for non-conservative planning.

ppp2pwa(self, region_index)

Return dynamics and predicate-preserving region and its index for PWA subsystem active in given region.

The returned region is the trans_set used for non-conservative planning.

Parameters:

region_index - index in ppp.regions.

Returns: (i, pwa.pwa_ppp[i])

ppp2sys(self, region_index)

Return index and PWA subsystem active in indexed region.

Semantics: j-th sub-system is active in i-th Region, where j = ppp2pwa[i]

Parameters:

region_index - index in ppp.regions.

Returns: (i, pwa.list_subsys[i])

ppp2orig(self, region_index)

Return index and region of original partition.

The original partition is w/o any dynamics, not even the PWA domains, only the polytopic predicates.

Parameters:

region_index - index in ppp.regions.

Returns: (i, orig_ppp.regions[i])

plot(self, show_ts=False, only_adjacent=False, color_seed=None)

Plot partition and optionally feasible transitions.

Parameters:

show_ts (bool) - plot feasible transitions on partition
only_adjacent - plot feasible transitions only between adjacent regions. This reduces clutter, but if horizon > 1 and not all horizon used, then some transitions could be hidden.
only_adjacent - bool

Class AbstractPwa

Notes

__init__(self, ppp=None, ts=None, ppp2ts=None, pwa=None, pwa_ppp=None, ppp2pwa=None, ppp2sys=None, orig_ppp=None, ppp2orig=None, disc_params=None) (Constructor)

__str__(self) (Informal representation operator)

ppp2trans(self, region_index)

ppp2pwa(self, region_index)

ppp2sys(self, region_index)

ppp2orig(self, region_index)

plot(self, show_ts=False, only_adjacent=False, color_seed=None)

init(self, ppp=None, ts=None, ppp2ts=None, pwa=None, pwa_ppp=None, ppp2pwa=None, ppp2sys=None, orig_ppp=None, ppp2orig=None, disc_params=None)
(Constructor)

str(self)
(Informal representation operator)